Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(140))\).
|
Total |
New |
Old |
Modular forms
| 126 |
38 |
88 |
Cusp forms
| 6 |
6 |
0 |
Eisenstein series
| 120 |
32 |
88 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)
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 available newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
140.1.b |
\(\chi_{140}(71, \cdot)\) |
None |
0 |
1 |
140.1.d |
\(\chi_{140}(41, \cdot)\) |
None |
0 |
1 |
140.1.f |
\(\chi_{140}(99, \cdot)\) |
None |
0 |
1 |
140.1.h |
\(\chi_{140}(69, \cdot)\) |
140.1.h.a |
1 |
1 |
140.1.h.b |
1 |
140.1.j |
\(\chi_{140}(27, \cdot)\) |
None |
0 |
2 |
140.1.l |
\(\chi_{140}(57, \cdot)\) |
None |
0 |
2 |
140.1.n |
\(\chi_{140}(89, \cdot)\) |
None |
0 |
2 |
140.1.p |
\(\chi_{140}(39, \cdot)\) |
140.1.p.a |
2 |
2 |
140.1.p.b |
2 |
140.1.r |
\(\chi_{140}(61, \cdot)\) |
None |
0 |
2 |
140.1.t |
\(\chi_{140}(11, \cdot)\) |
None |
0 |
2 |
140.1.v |
\(\chi_{140}(37, \cdot)\) |
None |
0 |
4 |
140.1.x |
\(\chi_{140}(3, \cdot)\) |
None |
0 |
4 |