Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(333))\).
|
Total |
New |
Old |
Modular forms
| 4392 |
3401 |
991 |
Cusp forms
| 3817 |
3087 |
730 |
Eisenstein series
| 575 |
314 |
261 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)
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 |
333.2.a |
\(\chi_{333}(1, \cdot)\) |
333.2.a.a |
1 |
1 |
333.2.a.b |
1 |
333.2.a.c |
1 |
333.2.a.d |
1 |
333.2.a.e |
3 |
333.2.a.f |
4 |
333.2.a.g |
4 |
333.2.c |
\(\chi_{333}(73, \cdot)\) |
333.2.c.a |
2 |
1 |
333.2.c.b |
2 |
333.2.c.c |
4 |
333.2.c.d |
8 |
333.2.e |
\(\chi_{333}(112, \cdot)\) |
333.2.e.a |
36 |
2 |
333.2.e.b |
36 |
333.2.f |
\(\chi_{333}(10, \cdot)\) |
333.2.f.a |
2 |
2 |
333.2.f.b |
6 |
333.2.f.c |
10 |
333.2.f.d |
12 |
333.2.g |
\(\chi_{333}(211, \cdot)\) |
333.2.g.a |
72 |
2 |
333.2.h |
\(\chi_{333}(121, \cdot)\) |
333.2.h.a |
72 |
2 |
333.2.j |
\(\chi_{333}(80, \cdot)\) |
333.2.j.a |
28 |
2 |
333.2.k |
\(\chi_{333}(175, \cdot)\) |
333.2.k.a |
2 |
2 |
333.2.k.b |
4 |
333.2.k.c |
66 |
333.2.q |
\(\chi_{333}(184, \cdot)\) |
333.2.q.a |
8 |
2 |
333.2.q.b |
12 |
333.2.q.c |
52 |
333.2.s |
\(\chi_{333}(64, \cdot)\) |
333.2.s.a |
2 |
2 |
333.2.s.b |
4 |
333.2.s.c |
4 |
333.2.s.d |
6 |
333.2.s.e |
8 |
333.2.s.f |
8 |
333.2.t |
\(\chi_{333}(85, \cdot)\) |
333.2.t.a |
2 |
2 |
333.2.t.b |
4 |
333.2.t.c |
66 |
333.2.w |
\(\chi_{333}(7, \cdot)\) |
333.2.w.a |
216 |
6 |
333.2.x |
\(\chi_{333}(46, \cdot)\) |
333.2.x.a |
6 |
6 |
333.2.x.b |
6 |
333.2.x.c |
6 |
333.2.x.d |
18 |
333.2.x.e |
24 |
333.2.x.f |
24 |
333.2.y |
\(\chi_{333}(16, \cdot)\) |
333.2.y.a |
216 |
6 |
333.2.z |
\(\chi_{333}(14, \cdot)\) |
333.2.z.a |
144 |
4 |
333.2.bc |
\(\chi_{333}(68, \cdot)\) |
333.2.bc.a |
144 |
4 |
333.2.be |
\(\chi_{333}(8, \cdot)\) |
333.2.be.a |
56 |
4 |
333.2.bf |
\(\chi_{333}(140, \cdot)\) |
333.2.bf.a |
144 |
4 |
333.2.bl |
\(\chi_{333}(28, \cdot)\) |
333.2.bl.a |
6 |
6 |
333.2.bl.b |
12 |
333.2.bl.c |
18 |
333.2.bl.d |
18 |
333.2.bl.e |
36 |
333.2.bm |
\(\chi_{333}(58, \cdot)\) |
333.2.bm.a |
216 |
6 |
333.2.bp |
\(\chi_{333}(4, \cdot)\) |
333.2.bp.a |
216 |
6 |
333.2.br |
\(\chi_{333}(17, \cdot)\) |
333.2.br.a |
144 |
12 |
333.2.bs |
\(\chi_{333}(56, \cdot)\) |
333.2.bs.a |
432 |
12 |
333.2.bv |
\(\chi_{333}(2, \cdot)\) |
333.2.bv.a |
432 |
12 |