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Properties

Label 2904.2
Level 2904
Weight 2
Dimension 95835
Nonzero newspaces 24
Sturm bound 929280
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2904 = 2^{3} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(929280\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2904))\).

Total New Old
Modular forms 236160 96959 139201
Cusp forms 228481 95835 132646
Eisenstein series 7679 1124 6555

Trace form

\( 95835 q - 2 q^{2} - 93 q^{3} - 184 q^{4} - 2 q^{5} - 88 q^{6} - 184 q^{7} + 4 q^{8} - 183 q^{9} + O(q^{10}) \) \( 95835 q - 2 q^{2} - 93 q^{3} - 184 q^{4} - 2 q^{5} - 88 q^{6} - 184 q^{7} + 4 q^{8} - 183 q^{9} - 176 q^{10} - 162 q^{12} - 2 q^{13} + 4 q^{14} - 104 q^{15} - 180 q^{16} - 42 q^{17} - 96 q^{18} - 240 q^{19} - 8 q^{20} - 40 q^{21} - 200 q^{22} - 40 q^{23} - 102 q^{24} - 449 q^{25} - 8 q^{26} - 81 q^{27} - 180 q^{28} - 34 q^{29} - 34 q^{30} - 208 q^{31} + 48 q^{32} - 185 q^{33} - 160 q^{34} + 120 q^{35} + 74 q^{36} + 6 q^{37} + 208 q^{38} + 24 q^{39} + 108 q^{40} + 118 q^{41} + 134 q^{42} - 36 q^{43} + 140 q^{44} + 58 q^{45} + 92 q^{46} + 96 q^{47} + 122 q^{48} - 239 q^{49} + 278 q^{50} + 22 q^{51} + 36 q^{52} - 2 q^{53} + 76 q^{54} - 140 q^{55} + 152 q^{56} - 62 q^{57} - 152 q^{58} + 4 q^{59} + 10 q^{60} - 2 q^{61} - 4 q^{62} - 6 q^{63} - 196 q^{64} + 20 q^{65} - 100 q^{66} - 316 q^{67} + 88 q^{69} - 468 q^{70} + 112 q^{71} - 118 q^{72} - 238 q^{73} - 184 q^{74} + 151 q^{75} - 524 q^{76} + 60 q^{77} - 402 q^{78} + 232 q^{79} - 440 q^{80} - 151 q^{81} - 616 q^{82} + 396 q^{83} - 338 q^{84} + 236 q^{85} - 328 q^{86} + 112 q^{87} - 520 q^{88} + 94 q^{89} - 134 q^{90} + 260 q^{91} - 320 q^{92} + 52 q^{93} - 636 q^{94} + 312 q^{95} - 326 q^{96} - 322 q^{97} - 434 q^{98} - 110 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2904))\)

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
2904.2.a \(\chi_{2904}(1, \cdot)\) 2904.2.a.a 1 1
2904.2.a.b 1
2904.2.a.c 1
2904.2.a.d 1
2904.2.a.e 1
2904.2.a.f 1
2904.2.a.g 1
2904.2.a.h 1
2904.2.a.i 1
2904.2.a.j 1
2904.2.a.k 1
2904.2.a.l 1
2904.2.a.m 1
2904.2.a.n 1
2904.2.a.o 1
2904.2.a.p 2
2904.2.a.q 2
2904.2.a.r 2
2904.2.a.s 2
2904.2.a.t 2
2904.2.a.u 2
2904.2.a.v 2
2904.2.a.w 2
2904.2.a.x 2
2904.2.a.y 2
2904.2.a.z 2
2904.2.a.ba 2
2904.2.a.bb 4
2904.2.a.bc 4
2904.2.a.bd 4
2904.2.a.be 4
2904.2.b \(\chi_{2904}(2177, \cdot)\) n/a 108 1
2904.2.d \(\chi_{2904}(2663, \cdot)\) None 0 1
2904.2.f \(\chi_{2904}(1453, \cdot)\) n/a 218 1
2904.2.h \(\chi_{2904}(2419, \cdot)\) n/a 216 1
2904.2.k \(\chi_{2904}(1211, \cdot)\) n/a 418 1
2904.2.m \(\chi_{2904}(725, \cdot)\) n/a 416 1
2904.2.o \(\chi_{2904}(967, \cdot)\) None 0 1
2904.2.q \(\chi_{2904}(1945, \cdot)\) n/a 216 4
2904.2.s \(\chi_{2904}(1183, \cdot)\) None 0 4
2904.2.u \(\chi_{2904}(941, \cdot)\) n/a 1664 4
2904.2.w \(\chi_{2904}(251, \cdot)\) n/a 1664 4
2904.2.z \(\chi_{2904}(403, \cdot)\) n/a 864 4
2904.2.bb \(\chi_{2904}(493, \cdot)\) n/a 864 4
2904.2.bd \(\chi_{2904}(1703, \cdot)\) None 0 4
2904.2.bf \(\chi_{2904}(161, \cdot)\) n/a 432 4
2904.2.bg \(\chi_{2904}(265, \cdot)\) n/a 660 10
2904.2.bi \(\chi_{2904}(175, \cdot)\) None 0 10
2904.2.bk \(\chi_{2904}(197, \cdot)\) n/a 5240 10
2904.2.bm \(\chi_{2904}(155, \cdot)\) n/a 5240 10
2904.2.bp \(\chi_{2904}(43, \cdot)\) n/a 2640 10
2904.2.br \(\chi_{2904}(133, \cdot)\) n/a 2640 10
2904.2.bt \(\chi_{2904}(23, \cdot)\) None 0 10
2904.2.bv \(\chi_{2904}(65, \cdot)\) n/a 1320 10
2904.2.bw \(\chi_{2904}(25, \cdot)\) n/a 2640 40
2904.2.bx \(\chi_{2904}(17, \cdot)\) n/a 5280 40
2904.2.bz \(\chi_{2904}(47, \cdot)\) None 0 40
2904.2.cb \(\chi_{2904}(37, \cdot)\) n/a 10560 40
2904.2.cd \(\chi_{2904}(19, \cdot)\) n/a 10560 40
2904.2.cg \(\chi_{2904}(59, \cdot)\) n/a 20960 40
2904.2.ci \(\chi_{2904}(29, \cdot)\) n/a 20960 40
2904.2.ck \(\chi_{2904}(7, \cdot)\) None 0 40

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2904))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2904)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1452))\)\(^{\oplus 2}\)