Defining specific controls for rotation.

I'm attempting to make a helicopter game. It'll be like the endless runners so I only want the helicopter to go up and down however, I would also like slight rotation along the z axis to give it that 'lift' 'drop' feel.

My current script gives my heli the rotation I am after however it's tied to the horizontal input (left right, a, d). Could someone advise me on the best way to achieve the following:

Helicopter rotates left (backwards slightly) and transforms upwards when space is pressed. And when released goes into 'falling' by translating downwards whilst also rotated slightly forward.

My script is below:

 using UnityEngine;
 using System.Collections;

 public class Helicontrol : MonoBehaviour {
 
 public float tiltAngle = 20.0f;
 public float smooth = 2.0f;
 // Use this for initialization
 void Start () {
 
 }
 
 // Update is called once per frame
 void Update () {
     //get the horizontal axis only
     
     float tiltAroundZ = Input.GetAxis("Horizontal") * tiltAngle;
     
     Quaternion target = Quaternion.Euler(0, 0, -tiltAroundZ);
     
     transform.rotation = Quaternion.Slerp(transform.rotation, target, Time.deltaTime * smooth);
     
     
         
  }
 }

Thank you for any help you can provide :)

Euden