Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(820))\).
|
Total |
New |
Old |
| Modular forms
| 20960 |
10998 |
9962 |
| Cusp forms
| 19361 |
10534 |
8827 |
| Eisenstein series
| 1599 |
464 |
1135 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(820))\)
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 available newforms together with their dimension.
| Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
| 820.2.a |
\(\chi_{820}(1, \cdot)\) |
820.2.a.a |
2 |
1 |
| 820.2.a.b |
2 |
| 820.2.a.c |
4 |
| 820.2.a.d |
4 |
| 820.2.b |
\(\chi_{820}(81, \cdot)\) |
820.2.b.a |
6 |
1 |
| 820.2.b.b |
8 |
| 820.2.d |
\(\chi_{820}(329, \cdot)\) |
820.2.d.a |
6 |
1 |
| 820.2.d.b |
14 |
| 820.2.g |
\(\chi_{820}(409, \cdot)\) |
820.2.g.a |
4 |
1 |
| 820.2.g.b |
16 |
| 820.2.j |
\(\chi_{820}(483, \cdot)\) |
820.2.j.a |
2 |
2 |
| 820.2.j.b |
2 |
| 820.2.j.c |
240 |
| 820.2.k |
\(\chi_{820}(83, \cdot)\) |
820.2.k.a |
4 |
2 |
| 820.2.k.b |
8 |
| 820.2.k.c |
108 |
| 820.2.k.d |
120 |
| 820.2.n |
\(\chi_{820}(9, \cdot)\) |
820.2.n.a |
44 |
2 |
| 820.2.p |
\(\chi_{820}(401, \cdot)\) |
820.2.p.a |
2 |
2 |
| 820.2.p.b |
2 |
| 820.2.p.c |
2 |
| 820.2.p.d |
8 |
| 820.2.p.e |
14 |
| 820.2.r |
\(\chi_{820}(163, \cdot)\) |
820.2.r.a |
2 |
2 |
| 820.2.r.b |
2 |
| 820.2.r.c |
16 |
| 820.2.r.d |
16 |
| 820.2.r.e |
208 |
| 820.2.s |
\(\chi_{820}(583, \cdot)\) |
820.2.s.a |
2 |
2 |
| 820.2.s.b |
2 |
| 820.2.s.c |
240 |
| 820.2.u |
\(\chi_{820}(141, \cdot)\) |
820.2.u.a |
24 |
4 |
| 820.2.u.b |
32 |
| 820.2.w |
\(\chi_{820}(79, \cdot)\) |
820.2.w.a |
4 |
4 |
| 820.2.w.b |
4 |
| 820.2.w.c |
8 |
| 820.2.w.d |
8 |
| 820.2.w.e |
464 |
| 820.2.x |
\(\chi_{820}(273, \cdot)\) |
820.2.x.a |
84 |
4 |
| 820.2.y |
\(\chi_{820}(137, \cdot)\) |
820.2.y.a |
84 |
4 |
| 820.2.bc |
\(\chi_{820}(191, \cdot)\) |
820.2.bc.a |
168 |
4 |
| 820.2.bc.b |
168 |
| 820.2.be |
\(\chi_{820}(469, \cdot)\) |
820.2.be.a |
80 |
4 |
| 820.2.bg |
\(\chi_{820}(441, \cdot)\) |
820.2.bg.a |
24 |
4 |
| 820.2.bg.b |
32 |
| 820.2.bi |
\(\chi_{820}(189, \cdot)\) |
820.2.bi.a |
80 |
4 |
| 820.2.bk |
\(\chi_{820}(43, \cdot)\) |
820.2.bk.a |
8 |
8 |
| 820.2.bk.b |
8 |
| 820.2.bk.c |
960 |
| 820.2.bm |
\(\chi_{820}(23, \cdot)\) |
820.2.bm.a |
8 |
8 |
| 820.2.bm.b |
8 |
| 820.2.bm.c |
960 |
| 820.2.bo |
\(\chi_{820}(21, \cdot)\) |
820.2.bo.a |
48 |
8 |
| 820.2.bo.b |
64 |
| 820.2.bq |
\(\chi_{820}(49, \cdot)\) |
820.2.bq.a |
176 |
8 |
| 820.2.bt |
\(\chi_{820}(223, \cdot)\) |
820.2.bt.a |
8 |
8 |
| 820.2.bt.b |
8 |
| 820.2.bt.c |
960 |
| 820.2.bv |
\(\chi_{820}(103, \cdot)\) |
820.2.bv.a |
8 |
8 |
| 820.2.bv.b |
8 |
| 820.2.bv.c |
960 |
| 820.2.bw |
\(\chi_{820}(11, \cdot)\) |
820.2.bw.a |
672 |
16 |
| 820.2.bw.b |
672 |
| 820.2.ca |
\(\chi_{820}(13, \cdot)\) |
820.2.ca.a |
336 |
16 |
| 820.2.cb |
\(\chi_{820}(157, \cdot)\) |
820.2.cb.a |
336 |
16 |
| 820.2.cc |
\(\chi_{820}(19, \cdot)\) |
820.2.cc.a |
16 |
16 |
| 820.2.cc.b |
16 |
| 820.2.cc.c |
16 |
| 820.2.cc.d |
16 |
| 820.2.cc.e |
16 |
| 820.2.cc.f |
16 |
| 820.2.cc.g |
1856 |
