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Properties

Label 3038.2
Level 3038
Weight 2
Dimension 90090
Nonzero newspaces 40
Sturm bound 1128960
Trace bound 6

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Defining parameters

Level: \( N \) = \( 3038 = 2 \cdot 7^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(1128960\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3038))\).

Total New Old
Modular forms 285840 90090 195750
Cusp forms 278641 90090 188551
Eisenstein series 7199 0 7199

Trace form

\( 90090 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 16 q^{6} + 16 q^{7} - 2 q^{8} + 30 q^{9} + O(q^{10}) \) \( 90090 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 16 q^{6} + 16 q^{7} - 2 q^{8} + 30 q^{9} + 12 q^{10} + 24 q^{11} + 12 q^{13} + 12 q^{14} + 48 q^{15} + 6 q^{16} + 60 q^{17} + 22 q^{18} + 48 q^{19} + 12 q^{20} + 52 q^{21} + 54 q^{22} + 78 q^{23} + 16 q^{24} + 112 q^{25} + 74 q^{26} + 186 q^{27} + 16 q^{28} + 96 q^{29} + 108 q^{30} + 84 q^{31} - 2 q^{32} + 156 q^{33} + 72 q^{34} + 84 q^{35} + 70 q^{36} + 62 q^{37} - 22 q^{38} + 18 q^{39} - 72 q^{40} - 30 q^{41} - 108 q^{42} - 38 q^{43} - 60 q^{44} - 264 q^{45} - 204 q^{46} - 120 q^{47} - 28 q^{48} - 236 q^{49} - 86 q^{50} - 150 q^{51} - 16 q^{52} - 6 q^{53} - 188 q^{54} - 216 q^{55} - 72 q^{56} + 66 q^{57} - 84 q^{58} - 42 q^{59} - 36 q^{60} + 50 q^{61} - 2 q^{62} + 72 q^{63} + 6 q^{64} + 258 q^{65} + 96 q^{66} + 150 q^{67} + 60 q^{68} + 282 q^{69} + 84 q^{70} + 204 q^{71} + 22 q^{72} + 186 q^{73} + 68 q^{74} + 408 q^{75} + 58 q^{76} + 168 q^{77} + 170 q^{78} + 262 q^{79} + 42 q^{80} + 150 q^{81} + 120 q^{82} + 186 q^{83} + 52 q^{84} + 168 q^{85} + 176 q^{86} + 72 q^{87} + 84 q^{88} + 138 q^{89} + 336 q^{90} + 20 q^{91} + 48 q^{92} + 132 q^{93} + 204 q^{94} + 144 q^{95} + 16 q^{96} + 118 q^{97} + 96 q^{98} + 126 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3038))\)

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
3038.2.a \(\chi_{3038}(1, \cdot)\) 3038.2.a.a 1 1
3038.2.a.b 1
3038.2.a.c 1
3038.2.a.d 1
3038.2.a.e 1
3038.2.a.f 1
3038.2.a.g 1
3038.2.a.h 1
3038.2.a.i 1
3038.2.a.j 1
3038.2.a.k 1
3038.2.a.l 1
3038.2.a.m 1
3038.2.a.n 1
3038.2.a.o 2
3038.2.a.p 2
3038.2.a.q 2
3038.2.a.r 2
3038.2.a.s 2
3038.2.a.t 2
3038.2.a.u 2
3038.2.a.v 2
3038.2.a.w 2
3038.2.a.x 2
3038.2.a.y 2
3038.2.a.z 2
3038.2.a.ba 2
3038.2.a.bb 3
3038.2.a.bc 3
3038.2.a.bd 3
3038.2.a.be 3
3038.2.a.bf 3
3038.2.a.bg 3
3038.2.a.bh 3
3038.2.a.bi 3
3038.2.a.bj 4
3038.2.a.bk 4
3038.2.a.bl 7
3038.2.a.bm 7
3038.2.a.bn 8
3038.2.a.bo 8
3038.2.d \(\chi_{3038}(3037, \cdot)\) n/a 104 1
3038.2.e \(\chi_{3038}(687, \cdot)\) n/a 220 2
3038.2.f \(\chi_{3038}(373, \cdot)\) n/a 200 2
3038.2.g \(\chi_{3038}(67, \cdot)\) n/a 212 2
3038.2.h \(\chi_{3038}(459, \cdot)\) n/a 212 2
3038.2.i \(\chi_{3038}(295, \cdot)\) n/a 432 4
3038.2.l \(\chi_{3038}(1587, \cdot)\) n/a 212 2
3038.2.m \(\chi_{3038}(1959, \cdot)\) n/a 216 2
3038.2.n \(\chi_{3038}(619, \cdot)\) n/a 216 2
3038.2.u \(\chi_{3038}(1979, \cdot)\) n/a 212 2
3038.2.v \(\chi_{3038}(435, \cdot)\) n/a 840 6
3038.2.w \(\chi_{3038}(587, \cdot)\) n/a 416 4
3038.2.z \(\chi_{3038}(433, \cdot)\) n/a 912 6
3038.2.bc \(\chi_{3038}(851, \cdot)\) n/a 848 8
3038.2.bd \(\chi_{3038}(165, \cdot)\) n/a 848 8
3038.2.be \(\chi_{3038}(655, \cdot)\) n/a 864 8
3038.2.bf \(\chi_{3038}(785, \cdot)\) n/a 880 8
3038.2.bg \(\chi_{3038}(25, \cdot)\) n/a 1800 12
3038.2.bh \(\chi_{3038}(149, \cdot)\) n/a 1800 12
3038.2.bi \(\chi_{3038}(249, \cdot)\) n/a 1680 12
3038.2.bj \(\chi_{3038}(211, \cdot)\) n/a 1776 12
3038.2.bk \(\chi_{3038}(509, \cdot)\) n/a 848 8
3038.2.br \(\chi_{3038}(215, \cdot)\) n/a 864 8
3038.2.bs \(\chi_{3038}(489, \cdot)\) n/a 864 8
3038.2.bt \(\chi_{3038}(117, \cdot)\) n/a 848 8
3038.2.bw \(\chi_{3038}(225, \cdot)\) n/a 3648 24
3038.2.bx \(\chi_{3038}(243, \cdot)\) n/a 1800 12
3038.2.ce \(\chi_{3038}(61, \cdot)\) n/a 1776 12
3038.2.cf \(\chi_{3038}(181, \cdot)\) n/a 1776 12
3038.2.cg \(\chi_{3038}(285, \cdot)\) n/a 1800 12
3038.2.cl \(\chi_{3038}(27, \cdot)\) n/a 3648 24
3038.2.cm \(\chi_{3038}(71, \cdot)\) n/a 7104 48
3038.2.cn \(\chi_{3038}(39, \cdot)\) n/a 7104 48
3038.2.co \(\chi_{3038}(107, \cdot)\) n/a 7200 48
3038.2.cp \(\chi_{3038}(9, \cdot)\) n/a 7200 48
3038.2.cs \(\chi_{3038}(73, \cdot)\) n/a 7200 48
3038.2.ct \(\chi_{3038}(13, \cdot)\) n/a 7104 48
3038.2.cu \(\chi_{3038}(89, \cdot)\) n/a 7104 48
3038.2.db \(\chi_{3038}(3, \cdot)\) n/a 7200 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3038))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(217))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(434))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1519))\)\(^{\oplus 2}\)