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Properties

Label 2808.1
Level 2808
Weight 1
Dimension 96
Nonzero newspaces 8
Newform subspaces 16
Sturm bound 435456
Trace bound 16

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Defining parameters

Level: \( N \) = \( 2808 = 2^{3} \cdot 3^{3} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 16 \)
Sturm bound: \(435456\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2808))\).

Total New Old
Modular forms 4868 800 4068
Cusp forms 548 96 452
Eisenstein series 4320 704 3616

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 68 0 28 0

Trace form

\( 96 q - 2 q^{4} - 2 q^{5} + O(q^{10}) \) \( 96 q - 2 q^{4} - 2 q^{5} + 8 q^{10} + 2 q^{11} + 2 q^{16} - 14 q^{19} + 8 q^{22} - 14 q^{25} + 24 q^{26} + 36 q^{30} + 2 q^{31} + 8 q^{34} + 12 q^{35} + 2 q^{37} - 6 q^{43} + 4 q^{46} - 4 q^{47} + 2 q^{49} + 4 q^{52} - 12 q^{55} - 4 q^{58} - 2 q^{59} - 4 q^{61} + 12 q^{62} - 2 q^{64} - 2 q^{65} + 8 q^{70} - 12 q^{73} - 18 q^{75} - 12 q^{76} - 12 q^{79} - 8 q^{82} - 2 q^{85} + 4 q^{89} - 8 q^{94} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2808))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2808.1.b \(\chi_{2808}(701, \cdot)\) 2808.1.b.a 1 1
2808.1.b.b 1
2808.1.b.c 1
2808.1.b.d 1
2808.1.b.e 8
2808.1.e \(\chi_{2808}(2107, \cdot)\) None 0 1
2808.1.f \(\chi_{2808}(1457, \cdot)\) None 0 1
2808.1.i \(\chi_{2808}(1351, \cdot)\) None 0 1
2808.1.k \(\chi_{2808}(703, \cdot)\) None 0 1
2808.1.l \(\chi_{2808}(2105, \cdot)\) None 0 1
2808.1.o \(\chi_{2808}(2755, \cdot)\) 2808.1.o.a 8 1
2808.1.p \(\chi_{2808}(53, \cdot)\) None 0 1
2808.1.u \(\chi_{2808}(109, \cdot)\) None 0 2
2808.1.v \(\chi_{2808}(1513, \cdot)\) None 0 2
2808.1.y \(\chi_{2808}(863, \cdot)\) None 0 2
2808.1.z \(\chi_{2808}(2267, \cdot)\) 2808.1.z.a 4 2
2808.1.z.b 4
2808.1.bc \(\chi_{2808}(1135, \cdot)\) None 0 2
2808.1.bf \(\chi_{2808}(809, \cdot)\) 2808.1.bf.a 4 2
2808.1.bg \(\chi_{2808}(1459, \cdot)\) None 0 2
2808.1.bj \(\chi_{2808}(485, \cdot)\) None 0 2
2808.1.bl \(\chi_{2808}(881, \cdot)\) None 0 2
2808.1.bm \(\chi_{2808}(1855, \cdot)\) None 0 2
2808.1.bo \(\chi_{2808}(1531, \cdot)\) None 0 2
2808.1.bq \(\chi_{2808}(989, \cdot)\) None 0 2
2808.1.bs \(\chi_{2808}(883, \cdot)\) 2808.1.bs.a 6 2
2808.1.bs.b 6
2808.1.bt \(\chi_{2808}(1205, \cdot)\) None 0 2
2808.1.bu \(\chi_{2808}(991, \cdot)\) None 0 2
2808.1.bw \(\chi_{2808}(233, \cdot)\) None 0 2
2808.1.bz \(\chi_{2808}(1639, \cdot)\) None 0 2
2808.1.cb \(\chi_{2808}(17, \cdot)\) None 0 2
2808.1.cc \(\chi_{2808}(341, \cdot)\) None 0 2
2808.1.cd \(\chi_{2808}(667, \cdot)\) None 0 2
2808.1.cf \(\chi_{2808}(451, \cdot)\) None 0 2
2808.1.ci \(\chi_{2808}(2285, \cdot)\) None 0 2
2808.1.ck \(\chi_{2808}(2609, \cdot)\) None 0 2
2808.1.cm \(\chi_{2808}(415, \cdot)\) None 0 2
2808.1.cn \(\chi_{2808}(521, \cdot)\) None 0 2
2808.1.cp \(\chi_{2808}(127, \cdot)\) None 0 2
2808.1.cs \(\chi_{2808}(413, \cdot)\) None 0 2
2808.1.cu \(\chi_{2808}(235, \cdot)\) None 0 2
2808.1.cv \(\chi_{2808}(1637, \cdot)\) None 0 2
2808.1.cx \(\chi_{2808}(1387, \cdot)\) None 0 2
2808.1.cz \(\chi_{2808}(1063, \cdot)\) None 0 2
2808.1.dc \(\chi_{2808}(737, \cdot)\) None 0 2
2808.1.dd \(\chi_{2808}(269, \cdot)\) 2808.1.dd.a 8 2
2808.1.de \(\chi_{2808}(595, \cdot)\) None 0 2
2808.1.dh \(\chi_{2808}(1889, \cdot)\) None 0 2
2808.1.di \(\chi_{2808}(55, \cdot)\) None 0 2
2808.1.dp \(\chi_{2808}(73, \cdot)\) 2808.1.dp.a 4 4
2808.1.dp.b 4
2808.1.dq \(\chi_{2808}(1045, \cdot)\) None 0 4
2808.1.dr \(\chi_{2808}(683, \cdot)\) None 0 4
2808.1.ds \(\chi_{2808}(1007, \cdot)\) None 0 4
2808.1.dx \(\chi_{2808}(323, \cdot)\) None 0 4
2808.1.dy \(\chi_{2808}(215, \cdot)\) None 0 4
2808.1.dz \(\chi_{2808}(71, \cdot)\) None 0 4
2808.1.ea \(\chi_{2808}(899, \cdot)\) None 0 4
2808.1.ed \(\chi_{2808}(145, \cdot)\) None 0 4
2808.1.ee \(\chi_{2808}(37, \cdot)\) None 0 4
2808.1.ej \(\chi_{2808}(865, \cdot)\) None 0 4
2808.1.ek \(\chi_{2808}(973, \cdot)\) None 0 4
2808.1.el \(\chi_{2808}(253, \cdot)\) None 0 4
2808.1.em \(\chi_{2808}(505, \cdot)\) None 0 4
2808.1.er \(\chi_{2808}(395, \cdot)\) None 0 4
2808.1.es \(\chi_{2808}(359, \cdot)\) None 0 4
2808.1.et \(\chi_{2808}(101, \cdot)\) None 0 6
2808.1.ev \(\chi_{2808}(113, \cdot)\) None 0 6
2808.1.ey \(\chi_{2808}(29, \cdot)\) None 0 6
2808.1.fa \(\chi_{2808}(329, \cdot)\) None 0 6
2808.1.fc \(\chi_{2808}(295, \cdot)\) None 0 6
2808.1.fe \(\chi_{2808}(43, \cdot)\) None 0 6
2808.1.ff \(\chi_{2808}(547, \cdot)\) None 0 6
2808.1.fh \(\chi_{2808}(103, \cdot)\) None 0 6
2808.1.fi \(\chi_{2808}(259, \cdot)\) 2808.1.fi.a 18 6
2808.1.fi.b 18
2808.1.fk \(\chi_{2808}(79, \cdot)\) None 0 6
2808.1.fm \(\chi_{2808}(511, \cdot)\) None 0 6
2808.1.fo \(\chi_{2808}(211, \cdot)\) None 0 6
2808.1.fp \(\chi_{2808}(257, \cdot)\) None 0 6
2808.1.fr \(\chi_{2808}(653, \cdot)\) None 0 6
2808.1.ft \(\chi_{2808}(77, \cdot)\) None 0 6
2808.1.fv \(\chi_{2808}(209, \cdot)\) None 0 6
2808.1.fy \(\chi_{2808}(365, \cdot)\) None 0 6
2808.1.ga \(\chi_{2808}(545, \cdot)\) None 0 6
2808.1.gc \(\chi_{2808}(185, \cdot)\) None 0 6
2808.1.ge \(\chi_{2808}(173, \cdot)\) None 0 6
2808.1.gf \(\chi_{2808}(139, \cdot)\) None 0 6
2808.1.gh \(\chi_{2808}(439, \cdot)\) None 0 6
2808.1.gi \(\chi_{2808}(355, \cdot)\) None 0 6
2808.1.gk \(\chi_{2808}(367, \cdot)\) None 0 6
2808.1.gn \(\chi_{2808}(409, \cdot)\) None 0 12
2808.1.go \(\chi_{2808}(85, \cdot)\) None 0 12
2808.1.gr \(\chi_{2808}(227, \cdot)\) None 0 12
2808.1.gs \(\chi_{2808}(47, \cdot)\) None 0 12
2808.1.gv \(\chi_{2808}(83, \cdot)\) None 0 12
2808.1.gw \(\chi_{2808}(167, \cdot)\) None 0 12
2808.1.gy \(\chi_{2808}(301, \cdot)\) None 0 12
2808.1.hb \(\chi_{2808}(265, \cdot)\) None 0 12
2808.1.hc \(\chi_{2808}(229, \cdot)\) None 0 12
2808.1.hf \(\chi_{2808}(97, \cdot)\) None 0 12
2808.1.hg \(\chi_{2808}(119, \cdot)\) None 0 12
2808.1.hj \(\chi_{2808}(11, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2808))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2808)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1404))\)\(^{\oplus 2}\)