Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1248))\).
|
Total |
New |
Old |
Modular forms
| 1716 |
252 |
1464 |
Cusp forms
| 180 |
32 |
148 |
Eisenstein series
| 1536 |
220 |
1316 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1248))\)
We only show spaces with odd 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 |
1248.1.b |
\(\chi_{1248}(1169, \cdot)\) |
1248.1.b.a |
4 |
1 |
1248.1.e |
\(\chi_{1248}(79, \cdot)\) |
None |
0 |
1 |
1248.1.f |
\(\chi_{1248}(833, \cdot)\) |
None |
0 |
1 |
1248.1.i |
\(\chi_{1248}(415, \cdot)\) |
None |
0 |
1 |
1248.1.k |
\(\chi_{1248}(703, \cdot)\) |
None |
0 |
1 |
1248.1.l |
\(\chi_{1248}(545, \cdot)\) |
1248.1.l.a |
4 |
1 |
1248.1.o |
\(\chi_{1248}(1039, \cdot)\) |
None |
0 |
1 |
1248.1.p |
\(\chi_{1248}(209, \cdot)\) |
None |
0 |
1 |
1248.1.s |
\(\chi_{1248}(551, \cdot)\) |
None |
0 |
2 |
1248.1.t |
\(\chi_{1248}(265, \cdot)\) |
None |
0 |
2 |
1248.1.w |
\(\chi_{1248}(521, \cdot)\) |
None |
0 |
2 |
1248.1.y |
\(\chi_{1248}(103, \cdot)\) |
None |
0 |
2 |
1248.1.z |
\(\chi_{1248}(1009, \cdot)\) |
None |
0 |
2 |
1248.1.ba |
\(\chi_{1248}(385, \cdot)\) |
None |
0 |
2 |
1248.1.bd |
\(\chi_{1248}(671, \cdot)\) |
None |
0 |
2 |
1248.1.be |
\(\chi_{1248}(47, \cdot)\) |
None |
0 |
2 |
1248.1.bi |
\(\chi_{1248}(233, \cdot)\) |
None |
0 |
2 |
1248.1.bk |
\(\chi_{1248}(391, \cdot)\) |
None |
0 |
2 |
1248.1.bl |
\(\chi_{1248}(73, \cdot)\) |
None |
0 |
2 |
1248.1.bo |
\(\chi_{1248}(359, \cdot)\) |
None |
0 |
2 |
1248.1.bp |
\(\chi_{1248}(127, \cdot)\) |
None |
0 |
2 |
1248.1.bs |
\(\chi_{1248}(737, \cdot)\) |
1248.1.bs.a |
8 |
2 |
1248.1.bt |
\(\chi_{1248}(367, \cdot)\) |
None |
0 |
2 |
1248.1.bw |
\(\chi_{1248}(17, \cdot)\) |
None |
0 |
2 |
1248.1.bx |
\(\chi_{1248}(113, \cdot)\) |
None |
0 |
2 |
1248.1.by |
\(\chi_{1248}(751, \cdot)\) |
None |
0 |
2 |
1248.1.cb |
\(\chi_{1248}(257, \cdot)\) |
None |
0 |
2 |
1248.1.cc |
\(\chi_{1248}(607, \cdot)\) |
None |
0 |
2 |
1248.1.ce |
\(\chi_{1248}(83, \cdot)\) |
None |
0 |
4 |
1248.1.cg |
\(\chi_{1248}(421, \cdot)\) |
None |
0 |
4 |
1248.1.cj |
\(\chi_{1248}(235, \cdot)\) |
None |
0 |
4 |
1248.1.cl |
\(\chi_{1248}(259, \cdot)\) |
None |
0 |
4 |
1248.1.cm |
\(\chi_{1248}(77, \cdot)\) |
1248.1.cm.a |
16 |
4 |
1248.1.co |
\(\chi_{1248}(53, \cdot)\) |
None |
0 |
4 |
1248.1.cr |
\(\chi_{1248}(395, \cdot)\) |
None |
0 |
4 |
1248.1.ct |
\(\chi_{1248}(109, \cdot)\) |
None |
0 |
4 |
1248.1.cv |
\(\chi_{1248}(457, \cdot)\) |
None |
0 |
4 |
1248.1.cw |
\(\chi_{1248}(71, \cdot)\) |
None |
0 |
4 |
1248.1.cy |
\(\chi_{1248}(55, \cdot)\) |
None |
0 |
4 |
1248.1.da |
\(\chi_{1248}(329, \cdot)\) |
None |
0 |
4 |
1248.1.de |
\(\chi_{1248}(431, \cdot)\) |
None |
0 |
4 |
1248.1.df |
\(\chi_{1248}(383, \cdot)\) |
None |
0 |
4 |
1248.1.di |
\(\chi_{1248}(97, \cdot)\) |
None |
0 |
4 |
1248.1.dj |
\(\chi_{1248}(145, \cdot)\) |
None |
0 |
4 |
1248.1.dk |
\(\chi_{1248}(199, \cdot)\) |
None |
0 |
4 |
1248.1.dm |
\(\chi_{1248}(185, \cdot)\) |
None |
0 |
4 |
1248.1.do |
\(\chi_{1248}(119, \cdot)\) |
None |
0 |
4 |
1248.1.dr |
\(\chi_{1248}(409, \cdot)\) |
None |
0 |
4 |
1248.1.ds |
\(\chi_{1248}(37, \cdot)\) |
None |
0 |
8 |
1248.1.du |
\(\chi_{1248}(323, \cdot)\) |
None |
0 |
8 |
1248.1.dw |
\(\chi_{1248}(101, \cdot)\) |
None |
0 |
8 |
1248.1.dy |
\(\chi_{1248}(29, \cdot)\) |
None |
0 |
8 |
1248.1.eb |
\(\chi_{1248}(139, \cdot)\) |
None |
0 |
8 |
1248.1.ed |
\(\chi_{1248}(43, \cdot)\) |
None |
0 |
8 |
1248.1.ef |
\(\chi_{1248}(349, \cdot)\) |
None |
0 |
8 |
1248.1.eh |
\(\chi_{1248}(11, \cdot)\) |
None |
0 |
8 |