(2,4,{(k-1)/4,(k+1)/4},±(-1)^(k/2))

Holomorphic, Degree 2, Level 4

• Weight 5 , 6 , 9 , 10 , 12 , 13 , 14 , 16 , 17 , 20 , 21 , 25 , 29 , 33 , 37 , 41 , 45 , 49 , . . .
• Hecke polynomials for T3

Back to Degree 2, Back to the start

has three cusps, so in general we expect the dimension of the space of modular forms to be greater by three than the space of cusp forms.

Let denote the non-trivial character mod 4. There is a weight 1 Eisenstein series in which is associated with

It is given by

It is well known that if

then is a modular form of weight 1 for . In fact,

For weight two there are two modular forms, one with a minus and one with a plus. These can be found from the modular form of weight two on . Thus,

and

Then,

Also,

is a weight 2 form. We find that

These give rise to three linearly independent modular forms of weight 4:

Note that there are two plusses and one minus modular form of weight 4.vel4.html