Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(475))\).
|
Total |
New |
Old |
Modular forms
| 9504 |
8598 |
906 |
Cusp forms
| 8497 |
7902 |
595 |
Eisenstein series
| 1007 |
696 |
311 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)
We only show spaces with even 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 |
475.2.a |
\(\chi_{475}(1, \cdot)\) |
475.2.a.a |
1 |
1 |
475.2.a.b |
1 |
475.2.a.c |
1 |
475.2.a.d |
3 |
475.2.a.e |
3 |
475.2.a.f |
3 |
475.2.a.g |
3 |
475.2.a.h |
3 |
475.2.a.i |
4 |
475.2.a.j |
6 |
475.2.b |
\(\chi_{475}(324, \cdot)\) |
475.2.b.a |
2 |
1 |
475.2.b.b |
6 |
475.2.b.c |
6 |
475.2.b.d |
6 |
475.2.b.e |
8 |
475.2.e |
\(\chi_{475}(26, \cdot)\) |
475.2.e.a |
2 |
2 |
475.2.e.b |
2 |
475.2.e.c |
2 |
475.2.e.d |
6 |
475.2.e.e |
8 |
475.2.e.f |
12 |
475.2.e.g |
12 |
475.2.e.h |
12 |
475.2.g |
\(\chi_{475}(18, \cdot)\) |
475.2.g.a |
4 |
2 |
475.2.g.b |
12 |
475.2.g.c |
16 |
475.2.g.d |
24 |
475.2.h |
\(\chi_{475}(96, \cdot)\) |
475.2.h.a |
84 |
4 |
475.2.h.b |
100 |
475.2.j |
\(\chi_{475}(49, \cdot)\) |
475.2.j.a |
4 |
2 |
475.2.j.b |
12 |
475.2.j.c |
16 |
475.2.j.d |
24 |
475.2.l |
\(\chi_{475}(101, \cdot)\) |
475.2.l.a |
6 |
6 |
475.2.l.b |
18 |
475.2.l.c |
18 |
475.2.l.d |
42 |
475.2.l.e |
42 |
475.2.l.f |
48 |
475.2.n |
\(\chi_{475}(39, \cdot)\) |
475.2.n.a |
80 |
4 |
475.2.n.b |
96 |
475.2.p |
\(\chi_{475}(107, \cdot)\) |
475.2.p.a |
4 |
4 |
475.2.p.b |
4 |
475.2.p.c |
4 |
475.2.p.d |
4 |
475.2.p.e |
16 |
475.2.p.f |
16 |
475.2.p.g |
16 |
475.2.p.h |
24 |
475.2.p.i |
24 |
475.2.r |
\(\chi_{475}(11, \cdot)\) |
475.2.r.a |
384 |
8 |
475.2.u |
\(\chi_{475}(24, \cdot)\) |
475.2.u.a |
12 |
6 |
475.2.u.b |
36 |
475.2.u.c |
36 |
475.2.u.d |
84 |
475.2.v |
\(\chi_{475}(37, \cdot)\) |
475.2.v.a |
16 |
8 |
475.2.v.b |
368 |
475.2.x |
\(\chi_{475}(64, \cdot)\) |
475.2.x.a |
384 |
8 |
475.2.bb |
\(\chi_{475}(32, \cdot)\) |
475.2.bb.a |
72 |
12 |
475.2.bb.b |
96 |
475.2.bb.c |
168 |
475.2.bc |
\(\chi_{475}(6, \cdot)\) |
475.2.bc.a |
1152 |
24 |
475.2.be |
\(\chi_{475}(8, \cdot)\) |
475.2.be.a |
768 |
16 |
475.2.bg |
\(\chi_{475}(4, \cdot)\) |
475.2.bg.a |
1152 |
24 |
475.2.bi |
\(\chi_{475}(2, \cdot)\) |
475.2.bi.a |
2304 |
48 |