Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1001))\).
|
Total |
New |
Old |
Modular forms
| 41760 |
38535 |
3225 |
Cusp forms
| 38881 |
36559 |
2322 |
Eisenstein series
| 2879 |
1976 |
903 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1001))\)
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 |
1001.2.a |
\(\chi_{1001}(1, \cdot)\) |
1001.2.a.a |
1 |
1 |
1001.2.a.b |
1 |
1001.2.a.c |
1 |
1001.2.a.d |
2 |
1001.2.a.e |
2 |
1001.2.a.f |
3 |
1001.2.a.g |
4 |
1001.2.a.h |
4 |
1001.2.a.i |
5 |
1001.2.a.j |
5 |
1001.2.a.k |
5 |
1001.2.a.l |
7 |
1001.2.a.m |
8 |
1001.2.a.n |
11 |
1001.2.b |
\(\chi_{1001}(846, \cdot)\) |
1001.2.b.a |
48 |
1 |
1001.2.b.b |
48 |
1001.2.d |
\(\chi_{1001}(155, \cdot)\) |
1001.2.d.a |
2 |
1 |
1001.2.d.b |
30 |
1001.2.d.c |
40 |
1001.2.g |
\(\chi_{1001}(1000, \cdot)\) |
n/a |
108 |
1 |
1001.2.i |
\(\chi_{1001}(144, \cdot)\) |
1001.2.i.a |
8 |
2 |
1001.2.i.b |
22 |
1001.2.i.c |
30 |
1001.2.i.d |
50 |
1001.2.i.e |
50 |
1001.2.j |
\(\chi_{1001}(386, \cdot)\) |
n/a |
136 |
2 |
1001.2.k |
\(\chi_{1001}(100, \cdot)\) |
n/a |
188 |
2 |
1001.2.l |
\(\chi_{1001}(529, \cdot)\) |
n/a |
188 |
2 |
1001.2.n |
\(\chi_{1001}(34, \cdot)\) |
n/a |
192 |
2 |
1001.2.p |
\(\chi_{1001}(736, \cdot)\) |
n/a |
168 |
2 |
1001.2.q |
\(\chi_{1001}(92, \cdot)\) |
n/a |
288 |
4 |
1001.2.s |
\(\chi_{1001}(23, \cdot)\) |
n/a |
188 |
2 |
1001.2.u |
\(\chi_{1001}(87, \cdot)\) |
n/a |
216 |
2 |
1001.2.v |
\(\chi_{1001}(10, \cdot)\) |
n/a |
216 |
2 |
1001.2.ba |
\(\chi_{1001}(285, \cdot)\) |
n/a |
216 |
2 |
1001.2.bc |
\(\chi_{1001}(153, \cdot)\) |
n/a |
216 |
2 |
1001.2.bf |
\(\chi_{1001}(516, \cdot)\) |
n/a |
216 |
2 |
1001.2.bg |
\(\chi_{1001}(309, \cdot)\) |
n/a |
144 |
2 |
1001.2.bi |
\(\chi_{1001}(298, \cdot)\) |
n/a |
184 |
2 |
1001.2.bk |
\(\chi_{1001}(230, \cdot)\) |
n/a |
216 |
2 |
1001.2.bm |
\(\chi_{1001}(131, \cdot)\) |
n/a |
192 |
2 |
1001.2.bp |
\(\chi_{1001}(452, \cdot)\) |
n/a |
188 |
2 |
1001.2.br |
\(\chi_{1001}(439, \cdot)\) |
n/a |
216 |
2 |
1001.2.bu |
\(\chi_{1001}(90, \cdot)\) |
n/a |
432 |
4 |
1001.2.bx |
\(\chi_{1001}(64, \cdot)\) |
n/a |
336 |
4 |
1001.2.bz |
\(\chi_{1001}(118, \cdot)\) |
n/a |
384 |
4 |
1001.2.cb |
\(\chi_{1001}(353, \cdot)\) |
n/a |
376 |
4 |
1001.2.cc |
\(\chi_{1001}(32, \cdot)\) |
n/a |
432 |
4 |
1001.2.ce |
\(\chi_{1001}(197, \cdot)\) |
n/a |
336 |
4 |
1001.2.cf |
\(\chi_{1001}(109, \cdot)\) |
n/a |
432 |
4 |
1001.2.ci |
\(\chi_{1001}(45, \cdot)\) |
n/a |
376 |
4 |
1001.2.ck |
\(\chi_{1001}(122, \cdot)\) |
n/a |
368 |
4 |
1001.2.cl |
\(\chi_{1001}(111, \cdot)\) |
n/a |
368 |
4 |
1001.2.cp |
\(\chi_{1001}(340, \cdot)\) |
n/a |
432 |
4 |
1001.2.cq |
\(\chi_{1001}(16, \cdot)\) |
n/a |
864 |
8 |
1001.2.cr |
\(\chi_{1001}(9, \cdot)\) |
n/a |
864 |
8 |
1001.2.cs |
\(\chi_{1001}(113, \cdot)\) |
n/a |
672 |
8 |
1001.2.ct |
\(\chi_{1001}(53, \cdot)\) |
n/a |
768 |
8 |
1001.2.cv |
\(\chi_{1001}(8, \cdot)\) |
n/a |
672 |
8 |
1001.2.cx |
\(\chi_{1001}(125, \cdot)\) |
n/a |
864 |
8 |
1001.2.cz |
\(\chi_{1001}(17, \cdot)\) |
n/a |
864 |
8 |
1001.2.db |
\(\chi_{1001}(179, \cdot)\) |
n/a |
864 |
8 |
1001.2.de |
\(\chi_{1001}(40, \cdot)\) |
n/a |
768 |
8 |
1001.2.dg |
\(\chi_{1001}(139, \cdot)\) |
n/a |
864 |
8 |
1001.2.di |
\(\chi_{1001}(25, \cdot)\) |
n/a |
864 |
8 |
1001.2.dk |
\(\chi_{1001}(36, \cdot)\) |
n/a |
672 |
8 |
1001.2.dl |
\(\chi_{1001}(61, \cdot)\) |
n/a |
864 |
8 |
1001.2.do |
\(\chi_{1001}(62, \cdot)\) |
n/a |
864 |
8 |
1001.2.dq |
\(\chi_{1001}(129, \cdot)\) |
n/a |
864 |
8 |
1001.2.dv |
\(\chi_{1001}(101, \cdot)\) |
n/a |
864 |
8 |
1001.2.dw |
\(\chi_{1001}(68, \cdot)\) |
n/a |
864 |
8 |
1001.2.dy |
\(\chi_{1001}(4, \cdot)\) |
n/a |
864 |
8 |
1001.2.eb |
\(\chi_{1001}(72, \cdot)\) |
n/a |
1728 |
16 |
1001.2.ec |
\(\chi_{1001}(5, \cdot)\) |
n/a |
1728 |
16 |
1001.2.ed |
\(\chi_{1001}(20, \cdot)\) |
n/a |
1728 |
16 |
1001.2.eg |
\(\chi_{1001}(59, \cdot)\) |
n/a |
1728 |
16 |
1001.2.ei |
\(\chi_{1001}(50, \cdot)\) |
n/a |
1344 |
16 |
1001.2.ej |
\(\chi_{1001}(18, \cdot)\) |
n/a |
1728 |
16 |
1001.2.em |
\(\chi_{1001}(2, \cdot)\) |
n/a |
1728 |
16 |
1001.2.ep |
\(\chi_{1001}(80, \cdot)\) |
n/a |
1728 |
16 |
"n/a" means that newforms for that character have not been added to the database yet