Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(225))\).
|
Total |
New |
Old |
Modular forms
| 226 |
94 |
132 |
Cusp forms
| 2 |
2 |
0 |
Eisenstein series
| 224 |
92 |
132 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)
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 |
225.1.c |
\(\chi_{225}(26, \cdot)\) |
None |
0 |
1 |
225.1.d |
\(\chi_{225}(224, \cdot)\) |
None |
0 |
1 |
225.1.g |
\(\chi_{225}(82, \cdot)\) |
225.1.g.a |
2 |
2 |
225.1.i |
\(\chi_{225}(74, \cdot)\) |
None |
0 |
2 |
225.1.j |
\(\chi_{225}(101, \cdot)\) |
None |
0 |
2 |
225.1.l |
\(\chi_{225}(44, \cdot)\) |
None |
0 |
4 |
225.1.n |
\(\chi_{225}(71, \cdot)\) |
None |
0 |
4 |
225.1.o |
\(\chi_{225}(7, \cdot)\) |
None |
0 |
4 |
225.1.r |
\(\chi_{225}(28, \cdot)\) |
None |
0 |
8 |
225.1.t |
\(\chi_{225}(11, \cdot)\) |
None |
0 |
8 |
225.1.v |
\(\chi_{225}(14, \cdot)\) |
None |
0 |
8 |
225.1.x |
\(\chi_{225}(13, \cdot)\) |
None |
0 |
16 |