Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8003))\).
|
Total |
New |
Old |
Modular forms
| 2675400 |
2673065 |
2335 |
Cusp forms
| 2659801 |
2657865 |
1936 |
Eisenstein series
| 15599 |
15200 |
399 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8003))\)
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 |
8003.2.a |
\(\chi_{8003}(1, \cdot)\) |
8003.2.a.a |
147 |
1 |
8003.2.a.b |
153 |
8003.2.a.c |
172 |
8003.2.a.d |
179 |
8003.2.b |
\(\chi_{8003}(6041, \cdot)\) |
n/a |
674 |
1 |
8003.2.e |
\(\chi_{8003}(1326, \cdot)\) |
n/a |
1316 |
2 |
8003.2.g |
\(\chi_{8003}(2415, \cdot)\) |
n/a |
1364 |
2 |
8003.2.h |
\(\chi_{8003}(5142, \cdot)\) |
n/a |
2640 |
4 |
8003.2.j |
\(\chi_{8003}(3656, \cdot)\) |
n/a |
1364 |
2 |
8003.2.m |
\(\chi_{8003}(3179, \cdot)\) |
n/a |
2728 |
4 |
8003.2.o |
\(\chi_{8003}(1090, \cdot)\) |
n/a |
2728 |
4 |
8003.2.q |
\(\chi_{8003}(152, \cdot)\) |
n/a |
8112 |
12 |
8003.2.r |
\(\chi_{8003}(1061, \cdot)\) |
n/a |
5264 |
8 |
8003.2.s |
\(\chi_{8003}(394, \cdot)\) |
n/a |
5456 |
8 |
8003.2.u |
\(\chi_{8003}(160, \cdot)\) |
n/a |
13200 |
20 |
8003.2.x |
\(\chi_{8003}(303, \cdot)\) |
n/a |
8088 |
12 |
8003.2.ba |
\(\chi_{8003}(105, \cdot)\) |
n/a |
5456 |
8 |
8003.2.bb |
\(\chi_{8003}(183, \cdot)\) |
n/a |
16368 |
24 |
8003.2.be |
\(\chi_{8003}(370, \cdot)\) |
n/a |
13640 |
20 |
8003.2.bf |
\(\chi_{8003}(603, \cdot)\) |
n/a |
16368 |
24 |
8003.2.bi |
\(\chi_{8003}(23, \cdot)\) |
n/a |
10912 |
16 |
8003.2.bj |
\(\chi_{8003}(819, \cdot)\) |
n/a |
32736 |
48 |
8003.2.bk |
\(\chi_{8003}(213, \cdot)\) |
n/a |
26320 |
40 |
8003.2.bm |
\(\chi_{8003}(269, \cdot)\) |
n/a |
16368 |
24 |
8003.2.bp |
\(\chi_{8003}(83, \cdot)\) |
n/a |
27280 |
40 |
8003.2.br |
\(\chi_{8003}(59, \cdot)\) |
n/a |
32736 |
48 |
8003.2.bt |
\(\chi_{8003}(423, \cdot)\) |
n/a |
27280 |
40 |
8003.2.bx |
\(\chi_{8003}(33, \cdot)\) |
n/a |
32736 |
48 |
8003.2.by |
\(\chi_{8003}(16, \cdot)\) |
n/a |
65472 |
96 |
8003.2.ca |
\(\chi_{8003}(87, \cdot)\) |
n/a |
65472 |
96 |
8003.2.cb |
\(\chi_{8003}(30, \cdot)\) |
n/a |
54560 |
80 |
8003.2.cd |
\(\chi_{8003}(44, \cdot)\) |
n/a |
163680 |
240 |
8003.2.ce |
\(\chi_{8003}(4, \cdot)\) |
n/a |
65472 |
96 |
8003.2.ci |
\(\chi_{8003}(9, \cdot)\) |
n/a |
163680 |
240 |
8003.2.ck |
\(\chi_{8003}(75, \cdot)\) |
n/a |
130944 |
192 |
8003.2.cm |
\(\chi_{8003}(10, \cdot)\) |
n/a |
327360 |
480 |
8003.2.cn |
\(\chi_{8003}(3, \cdot)\) |
n/a |
327360 |
480 |
8003.2.cq |
\(\chi_{8003}(11, \cdot)\) |
n/a |
327360 |
480 |
8003.2.ct |
\(\chi_{8003}(12, \cdot)\) |
n/a |
654720 |
960 |
"n/a" means that newforms for that character have not been added to the database yet