Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1067))\).
|
Total |
New |
Old |
Modular forms
| 1011 |
905 |
106 |
Cusp forms
| 51 |
51 |
0 |
Eisenstein series
| 960 |
854 |
106 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1067))\)
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 |
1067.1.b |
\(\chi_{1067}(1066, \cdot)\) |
1067.1.b.a |
1 |
1 |
1067.1.b.b |
1 |
1067.1.b.c |
1 |
1067.1.b.d |
2 |
1067.1.c |
\(\chi_{1067}(98, \cdot)\) |
None |
0 |
1 |
1067.1.g |
\(\chi_{1067}(560, \cdot)\) |
1067.1.g.a |
2 |
2 |
1067.1.j |
\(\chi_{1067}(714, \cdot)\) |
1067.1.j.a |
2 |
2 |
1067.1.k |
\(\chi_{1067}(230, \cdot)\) |
1067.1.k.a |
2 |
2 |
1067.1.l |
\(\chi_{1067}(241, \cdot)\) |
1067.1.l.a |
4 |
4 |
1067.1.o |
\(\chi_{1067}(195, \cdot)\) |
None |
0 |
4 |
1067.1.p |
\(\chi_{1067}(96, \cdot)\) |
None |
0 |
4 |
1067.1.q |
\(\chi_{1067}(285, \cdot)\) |
1067.1.q.a |
4 |
4 |
1067.1.u |
\(\chi_{1067}(109, \cdot)\) |
1067.1.u.a |
8 |
8 |
1067.1.v |
\(\chi_{1067}(172, \cdot)\) |
None |
0 |
8 |
1067.1.y |
\(\chi_{1067}(43, \cdot)\) |
1067.1.y.a |
8 |
8 |
1067.1.z |
\(\chi_{1067}(62, \cdot)\) |
None |
0 |
8 |
1067.1.ba |
\(\chi_{1067}(35, \cdot)\) |
None |
0 |
8 |
1067.1.bd |
\(\chi_{1067}(34, \cdot)\) |
None |
0 |
16 |
1067.1.bf |
\(\chi_{1067}(50, \cdot)\) |
None |
0 |
16 |
1067.1.bg |
\(\chi_{1067}(32, \cdot)\) |
1067.1.bg.a |
16 |
16 |
1067.1.bj |
\(\chi_{1067}(6, \cdot)\) |
None |
0 |
16 |
1067.1.bk |
\(\chi_{1067}(8, \cdot)\) |
None |
0 |
32 |
1067.1.bm |
\(\chi_{1067}(23, \cdot)\) |
None |
0 |
32 |
1067.1.bo |
\(\chi_{1067}(24, \cdot)\) |
None |
0 |
32 |
1067.1.bq |
\(\chi_{1067}(20, \cdot)\) |
None |
0 |
64 |
1067.1.bt |
\(\chi_{1067}(2, \cdot)\) |
None |
0 |
64 |
1067.1.bv |
\(\chi_{1067}(5, \cdot)\) |
None |
0 |
128 |