Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1339))\).
|
Total |
New |
Old |
Modular forms
| 75480 |
74469 |
1011 |
Cusp forms
| 73033 |
72245 |
788 |
Eisenstein series
| 2447 |
2224 |
223 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1339))\)
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 |
1339.2.a |
\(\chi_{1339}(1, \cdot)\) |
1339.2.a.a |
1 |
1 |
1339.2.a.b |
1 |
1339.2.a.c |
3 |
1339.2.a.d |
19 |
1339.2.a.e |
21 |
1339.2.a.f |
28 |
1339.2.a.g |
30 |
1339.2.c |
\(\chi_{1339}(207, \cdot)\) |
n/a |
118 |
1 |
1339.2.e |
\(\chi_{1339}(458, \cdot)\) |
n/a |
238 |
2 |
1339.2.f |
\(\chi_{1339}(516, \cdot)\) |
n/a |
240 |
2 |
1339.2.g |
\(\chi_{1339}(365, \cdot)\) |
n/a |
208 |
2 |
1339.2.h |
\(\chi_{1339}(159, \cdot)\) |
n/a |
238 |
2 |
1339.2.i |
\(\chi_{1339}(411, \cdot)\) |
n/a |
236 |
2 |
1339.2.k |
\(\chi_{1339}(355, \cdot)\) |
n/a |
238 |
2 |
1339.2.q |
\(\chi_{1339}(413, \cdot)\) |
n/a |
236 |
2 |
1339.2.r |
\(\chi_{1339}(56, \cdot)\) |
n/a |
238 |
2 |
1339.2.u |
\(\chi_{1339}(571, \cdot)\) |
n/a |
240 |
2 |
1339.2.w |
\(\chi_{1339}(47, \cdot)\) |
n/a |
480 |
4 |
1339.2.ba |
\(\chi_{1339}(665, \cdot)\) |
n/a |
476 |
4 |
1339.2.bb |
\(\chi_{1339}(150, \cdot)\) |
n/a |
476 |
4 |
1339.2.bc |
\(\chi_{1339}(102, \cdot)\) |
n/a |
480 |
4 |
1339.2.be |
\(\chi_{1339}(14, \cdot)\) |
n/a |
1664 |
16 |
1339.2.bg |
\(\chi_{1339}(64, \cdot)\) |
n/a |
1888 |
16 |
1339.2.bi |
\(\chi_{1339}(107, \cdot)\) |
n/a |
3808 |
32 |
1339.2.bj |
\(\chi_{1339}(92, \cdot)\) |
n/a |
3328 |
32 |
1339.2.bk |
\(\chi_{1339}(9, \cdot)\) |
n/a |
3840 |
32 |
1339.2.bl |
\(\chi_{1339}(16, \cdot)\) |
n/a |
3808 |
32 |
1339.2.bn |
\(\chi_{1339}(31, \cdot)\) |
n/a |
3776 |
32 |
1339.2.bp |
\(\chi_{1339}(25, \cdot)\) |
n/a |
3840 |
32 |
1339.2.bs |
\(\chi_{1339}(4, \cdot)\) |
n/a |
3808 |
32 |
1339.2.bt |
\(\chi_{1339}(23, \cdot)\) |
n/a |
3840 |
32 |
1339.2.bz |
\(\chi_{1339}(36, \cdot)\) |
n/a |
3808 |
32 |
1339.2.cb |
\(\chi_{1339}(24, \cdot)\) |
n/a |
7680 |
64 |
1339.2.cc |
\(\chi_{1339}(45, \cdot)\) |
n/a |
7616 |
64 |
1339.2.cd |
\(\chi_{1339}(6, \cdot)\) |
n/a |
7616 |
64 |
1339.2.ch |
\(\chi_{1339}(5, \cdot)\) |
n/a |
7680 |
64 |
"n/a" means that newforms for that character have not been added to the database yet