Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(441))\).
|
Total |
New |
Old |
Modular forms
| 7536 |
5579 |
1957 |
Cusp forms
| 6577 |
5142 |
1435 |
Eisenstein series
| 959 |
437 |
522 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)
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 |
441.2.a |
\(\chi_{441}(1, \cdot)\) |
441.2.a.a |
1 |
1 |
441.2.a.b |
1 |
441.2.a.c |
1 |
441.2.a.d |
1 |
441.2.a.e |
1 |
441.2.a.f |
1 |
441.2.a.g |
2 |
441.2.a.h |
2 |
441.2.a.i |
2 |
441.2.a.j |
2 |
441.2.c |
\(\chi_{441}(440, \cdot)\) |
441.2.c.a |
4 |
1 |
441.2.c.b |
8 |
441.2.e |
\(\chi_{441}(226, \cdot)\) |
441.2.e.a |
2 |
2 |
441.2.e.b |
2 |
441.2.e.c |
2 |
441.2.e.d |
2 |
441.2.e.e |
2 |
441.2.e.f |
4 |
441.2.e.g |
4 |
441.2.e.h |
4 |
441.2.e.i |
4 |
441.2.e.j |
4 |
441.2.f |
\(\chi_{441}(148, \cdot)\) |
441.2.f.a |
2 |
2 |
441.2.f.b |
2 |
441.2.f.c |
6 |
441.2.f.d |
6 |
441.2.f.e |
10 |
441.2.f.f |
10 |
441.2.f.g |
12 |
441.2.f.h |
24 |
441.2.g |
\(\chi_{441}(67, \cdot)\) |
441.2.g.a |
2 |
2 |
441.2.g.b |
6 |
441.2.g.c |
6 |
441.2.g.d |
6 |
441.2.g.e |
6 |
441.2.g.f |
10 |
441.2.g.g |
12 |
441.2.g.h |
24 |
441.2.h |
\(\chi_{441}(214, \cdot)\) |
441.2.h.a |
2 |
2 |
441.2.h.b |
6 |
441.2.h.c |
6 |
441.2.h.d |
6 |
441.2.h.e |
6 |
441.2.h.f |
10 |
441.2.h.g |
12 |
441.2.h.h |
24 |
441.2.i |
\(\chi_{441}(68, \cdot)\) |
441.2.i.a |
2 |
2 |
441.2.i.b |
10 |
441.2.i.c |
12 |
441.2.i.d |
48 |
441.2.o |
\(\chi_{441}(146, \cdot)\) |
441.2.o.a |
2 |
2 |
441.2.o.b |
2 |
441.2.o.c |
10 |
441.2.o.d |
10 |
441.2.o.e |
48 |
441.2.p |
\(\chi_{441}(80, \cdot)\) |
441.2.p.a |
4 |
2 |
441.2.p.b |
8 |
441.2.p.c |
16 |
441.2.s |
\(\chi_{441}(362, \cdot)\) |
441.2.s.a |
2 |
2 |
441.2.s.b |
10 |
441.2.s.c |
12 |
441.2.s.d |
48 |
441.2.u |
\(\chi_{441}(64, \cdot)\) |
441.2.u.a |
6 |
6 |
441.2.u.b |
12 |
441.2.u.c |
24 |
441.2.u.d |
36 |
441.2.u.e |
60 |
441.2.w |
\(\chi_{441}(62, \cdot)\) |
441.2.w.a |
120 |
6 |
441.2.y |
\(\chi_{441}(25, \cdot)\) |
441.2.y.a |
648 |
12 |
441.2.z |
\(\chi_{441}(4, \cdot)\) |
441.2.z.a |
648 |
12 |
441.2.ba |
\(\chi_{441}(22, \cdot)\) |
441.2.ba.a |
648 |
12 |
441.2.bb |
\(\chi_{441}(37, \cdot)\) |
441.2.bb.a |
12 |
12 |
441.2.bb.b |
24 |
441.2.bb.c |
48 |
441.2.bb.d |
48 |
441.2.bb.e |
60 |
441.2.bb.f |
72 |
441.2.bd |
\(\chi_{441}(47, \cdot)\) |
441.2.bd.a |
648 |
12 |
441.2.bg |
\(\chi_{441}(17, \cdot)\) |
441.2.bg.a |
216 |
12 |
441.2.bh |
\(\chi_{441}(20, \cdot)\) |
441.2.bh.a |
648 |
12 |
441.2.bn |
\(\chi_{441}(5, \cdot)\) |
441.2.bn.a |
648 |
12 |