Properties

Label 1904.2
Level 1904
Weight 2
Dimension 58526
Nonzero newspaces 52
Sturm bound 442368
Trace bound 61

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Defining parameters

Level: \( N \) = \( 1904 = 2^{4} \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 52 \)
Sturm bound: \(442368\)
Trace bound: \(61\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1904))\).

Total New Old
Modular forms 113280 59878 53402
Cusp forms 107905 58526 49379
Eisenstein series 5375 1352 4023

Trace form

\( 58526 q - 112 q^{2} - 86 q^{3} - 104 q^{4} - 138 q^{5} - 88 q^{6} - 102 q^{7} - 256 q^{8} - 26 q^{9} + O(q^{10}) \) \( 58526 q - 112 q^{2} - 86 q^{3} - 104 q^{4} - 138 q^{5} - 88 q^{6} - 102 q^{7} - 256 q^{8} - 26 q^{9} - 104 q^{10} - 70 q^{11} - 120 q^{12} - 132 q^{13} - 144 q^{14} - 188 q^{15} - 136 q^{16} - 269 q^{17} - 224 q^{18} - 42 q^{19} - 88 q^{20} - 138 q^{21} - 272 q^{22} - 42 q^{23} - 104 q^{24} + 22 q^{25} - 88 q^{26} - 68 q^{27} - 120 q^{28} - 292 q^{29} - 120 q^{30} - 94 q^{31} - 72 q^{32} - 186 q^{33} - 108 q^{34} - 194 q^{35} - 288 q^{36} - 82 q^{37} - 152 q^{38} - 84 q^{39} - 136 q^{40} - 20 q^{41} - 280 q^{42} - 176 q^{43} - 216 q^{44} - 200 q^{45} - 176 q^{46} - 50 q^{47} - 312 q^{48} - 362 q^{49} - 464 q^{50} - 109 q^{51} - 464 q^{52} - 234 q^{53} - 440 q^{54} - 60 q^{55} - 320 q^{56} - 132 q^{57} - 320 q^{58} - 54 q^{59} - 440 q^{60} - 170 q^{61} - 256 q^{62} - 10 q^{63} - 440 q^{64} - 156 q^{65} - 328 q^{66} - 62 q^{67} - 176 q^{68} - 124 q^{69} - 216 q^{70} - 48 q^{71} - 280 q^{72} + 150 q^{73} - 104 q^{74} + 312 q^{75} - 56 q^{76} - 2 q^{77} - 288 q^{78} + 102 q^{79} - 72 q^{80} + 48 q^{81} - 104 q^{82} + 112 q^{83} - 152 q^{84} - 282 q^{85} - 232 q^{86} + 12 q^{87} - 72 q^{88} + 70 q^{89} + 24 q^{90} - 220 q^{91} - 344 q^{92} + 6 q^{93} - 24 q^{94} - 198 q^{95} + 72 q^{96} - 196 q^{97} - 8 q^{98} - 488 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1904))\)

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
1904.2.a \(\chi_{1904}(1, \cdot)\) 1904.2.a.a 1 1
1904.2.a.b 1
1904.2.a.c 1
1904.2.a.d 1
1904.2.a.e 1
1904.2.a.f 2
1904.2.a.g 2
1904.2.a.h 2
1904.2.a.i 2
1904.2.a.j 2
1904.2.a.k 2
1904.2.a.l 2
1904.2.a.m 3
1904.2.a.n 3
1904.2.a.o 3
1904.2.a.p 3
1904.2.a.q 4
1904.2.a.r 4
1904.2.a.s 4
1904.2.a.t 5
1904.2.b \(\chi_{1904}(953, \cdot)\) None 0 1
1904.2.c \(\chi_{1904}(1121, \cdot)\) 1904.2.c.a 2 1
1904.2.c.b 2
1904.2.c.c 4
1904.2.c.d 4
1904.2.c.e 6
1904.2.c.f 8
1904.2.c.g 8
1904.2.c.h 10
1904.2.c.i 10
1904.2.h \(\chi_{1904}(1903, \cdot)\) 1904.2.h.a 8 1
1904.2.h.b 16
1904.2.h.c 48
1904.2.i \(\chi_{1904}(1735, \cdot)\) None 0 1
1904.2.j \(\chi_{1904}(783, \cdot)\) 1904.2.j.a 8 1
1904.2.j.b 24
1904.2.j.c 32
1904.2.k \(\chi_{1904}(951, \cdot)\) None 0 1
1904.2.p \(\chi_{1904}(169, \cdot)\) None 0 1
1904.2.q \(\chi_{1904}(1089, \cdot)\) n/a 128 2
1904.2.s \(\chi_{1904}(1203, \cdot)\) n/a 568 2
1904.2.t \(\chi_{1904}(1373, \cdot)\) n/a 432 2
1904.2.w \(\chi_{1904}(1177, \cdot)\) None 0 2
1904.2.x \(\chi_{1904}(1007, \cdot)\) n/a 144 2
1904.2.z \(\chi_{1904}(475, \cdot)\) n/a 568 2
1904.2.bc \(\chi_{1904}(307, \cdot)\) n/a 512 2
1904.2.be \(\chi_{1904}(477, \cdot)\) n/a 384 2
1904.2.bf \(\chi_{1904}(645, \cdot)\) n/a 432 2
1904.2.bi \(\chi_{1904}(225, \cdot)\) n/a 108 2
1904.2.bj \(\chi_{1904}(55, \cdot)\) None 0 2
1904.2.bm \(\chi_{1904}(421, \cdot)\) n/a 432 2
1904.2.bn \(\chi_{1904}(251, \cdot)\) n/a 568 2
1904.2.bp \(\chi_{1904}(1257, \cdot)\) None 0 2
1904.2.bu \(\chi_{1904}(1055, \cdot)\) n/a 128 2
1904.2.bv \(\chi_{1904}(1223, \cdot)\) None 0 2
1904.2.bw \(\chi_{1904}(271, \cdot)\) n/a 144 2
1904.2.bx \(\chi_{1904}(103, \cdot)\) None 0 2
1904.2.cc \(\chi_{1904}(137, \cdot)\) None 0 2
1904.2.cd \(\chi_{1904}(305, \cdot)\) n/a 140 2
1904.2.ce \(\chi_{1904}(1063, \cdot)\) None 0 4
1904.2.cg \(\chi_{1904}(1233, \cdot)\) n/a 216 4
1904.2.ci \(\chi_{1904}(83, \cdot)\) n/a 1136 4
1904.2.ck \(\chi_{1904}(253, \cdot)\) n/a 864 4
1904.2.cm \(\chi_{1904}(195, \cdot)\) n/a 1136 4
1904.2.co \(\chi_{1904}(365, \cdot)\) n/a 864 4
1904.2.cq \(\chi_{1904}(111, \cdot)\) n/a 288 4
1904.2.cs \(\chi_{1904}(281, \cdot)\) None 0 4
1904.2.cv \(\chi_{1904}(523, \cdot)\) n/a 1136 4
1904.2.cw \(\chi_{1904}(149, \cdot)\) n/a 1136 4
1904.2.cy \(\chi_{1904}(361, \cdot)\) None 0 4
1904.2.db \(\chi_{1904}(47, \cdot)\) n/a 288 4
1904.2.dc \(\chi_{1904}(171, \cdot)\) n/a 1024 4
1904.2.df \(\chi_{1904}(339, \cdot)\) n/a 1136 4
1904.2.dh \(\chi_{1904}(373, \cdot)\) n/a 1136 4
1904.2.di \(\chi_{1904}(205, \cdot)\) n/a 1024 4
1904.2.dk \(\chi_{1904}(81, \cdot)\) n/a 280 4
1904.2.dn \(\chi_{1904}(327, \cdot)\) None 0 4
1904.2.dp \(\chi_{1904}(557, \cdot)\) n/a 1136 4
1904.2.dq \(\chi_{1904}(115, \cdot)\) n/a 1136 4
1904.2.dt \(\chi_{1904}(99, \cdot)\) n/a 1728 8
1904.2.dv \(\chi_{1904}(125, \cdot)\) n/a 2272 8
1904.2.dw \(\chi_{1904}(71, \cdot)\) None 0 8
1904.2.dz \(\chi_{1904}(351, \cdot)\) n/a 432 8
1904.2.ea \(\chi_{1904}(97, \cdot)\) n/a 560 8
1904.2.ed \(\chi_{1904}(41, \cdot)\) None 0 8
1904.2.ef \(\chi_{1904}(211, \cdot)\) n/a 1728 8
1904.2.eh \(\chi_{1904}(181, \cdot)\) n/a 2272 8
1904.2.ej \(\chi_{1904}(417, \cdot)\) n/a 560 8
1904.2.el \(\chi_{1904}(87, \cdot)\) None 0 8
1904.2.en \(\chi_{1904}(53, \cdot)\) n/a 2272 8
1904.2.ep \(\chi_{1904}(451, \cdot)\) n/a 2272 8
1904.2.er \(\chi_{1904}(485, \cdot)\) n/a 2272 8
1904.2.et \(\chi_{1904}(19, \cdot)\) n/a 2272 8
1904.2.ev \(\chi_{1904}(9, \cdot)\) None 0 8
1904.2.ex \(\chi_{1904}(383, \cdot)\) n/a 576 8
1904.2.ey \(\chi_{1904}(5, \cdot)\) n/a 4544 16
1904.2.fa \(\chi_{1904}(11, \cdot)\) n/a 4544 16
1904.2.fd \(\chi_{1904}(73, \cdot)\) None 0 16
1904.2.fe \(\chi_{1904}(129, \cdot)\) n/a 1120 16
1904.2.fh \(\chi_{1904}(79, \cdot)\) n/a 1152 16
1904.2.fi \(\chi_{1904}(23, \cdot)\) None 0 16
1904.2.fk \(\chi_{1904}(173, \cdot)\) n/a 4544 16
1904.2.fm \(\chi_{1904}(107, \cdot)\) n/a 4544 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1904))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1904)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(952))\)\(^{\oplus 2}\)