Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(63))\).

Total 
New 
Old 
Modular forms
 49 
24 
25 
Cusp forms
 1 
1 
0 
Eisenstein series
 48 
23 
25 
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.
Label 
\(\chi\) 
Newforms 
Dimension 
\(\chi\) degree 
63.1.b 
\(\chi_{63}(8, \cdot)\) 
None 
0 
1 
63.1.d 
\(\chi_{63}(55, \cdot)\) 
63.1.d.a 
1 
1 
63.1.j 
\(\chi_{63}(11, \cdot)\) 
None 
0 
2 
63.1.k 
\(\chi_{63}(31, \cdot)\) 
None 
0 
2 
63.1.l 
\(\chi_{63}(13, \cdot)\) 
None 
0 
2 
63.1.m 
\(\chi_{63}(10, \cdot)\) 
None 
0 
2 
63.1.n 
\(\chi_{63}(2, \cdot)\) 
None 
0 
2 
63.1.q 
\(\chi_{63}(44, \cdot)\) 
None 
0 
2 
63.1.r 
\(\chi_{63}(29, \cdot)\) 
None 
0 
2 
63.1.t 
\(\chi_{63}(40, \cdot)\) 
None 
0 
2 