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Properties

Label 3610.2
Level 3610
Weight 2
Dimension 118469
Nonzero newspaces 18
Sturm bound 1559520
Trace bound 4

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Defining parameters

Level: \( N \) = \( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(1559520\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3610))\).

Total New Old
Modular forms 393912 118469 275443
Cusp forms 385849 118469 267380
Eisenstein series 8063 0 8063

Trace form

\( 118469 q - q^{2} - 4 q^{3} - q^{4} - q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 118469 q - q^{2} - 4 q^{3} - q^{4} - q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - q^{10} - 12 q^{11} + 20 q^{12} + 82 q^{13} + 64 q^{14} + 68 q^{15} - q^{16} + 54 q^{17} + 95 q^{18} + 84 q^{19} + 35 q^{20} + 136 q^{21} + 96 q^{22} + 48 q^{23} - 4 q^{24} + 71 q^{25} + 58 q^{26} + 92 q^{27} + 16 q^{28} + 42 q^{29} - 4 q^{30} + 40 q^{31} - q^{32} + 168 q^{33} - 18 q^{34} + 64 q^{35} - 13 q^{36} + 34 q^{37} + 160 q^{39} - q^{40} + 30 q^{41} - 32 q^{42} + 124 q^{43} + 24 q^{44} + 203 q^{45} + 120 q^{46} + 240 q^{47} + 32 q^{48} + 183 q^{49} + 143 q^{50} + 324 q^{51} + 10 q^{52} + 234 q^{53} + 176 q^{54} + 132 q^{55} + 136 q^{56} + 180 q^{57} + 114 q^{58} + 300 q^{59} + 68 q^{60} + 250 q^{61} + 184 q^{62} + 280 q^{63} + 23 q^{64} + 202 q^{65} + 240 q^{66} + 244 q^{67} + 18 q^{68} + 120 q^{69} + 64 q^{70} + 216 q^{71} + 23 q^{72} + 58 q^{73} - 38 q^{74} + 20 q^{75} - 96 q^{77} - 200 q^{78} - 56 q^{79} - q^{80} - 301 q^{81} - 186 q^{82} - 228 q^{83} - 248 q^{84} - 450 q^{85} - 188 q^{86} - 552 q^{87} - 12 q^{88} - 234 q^{89} - 553 q^{90} - 304 q^{91} - 168 q^{92} - 680 q^{93} - 336 q^{94} - 126 q^{95} - 4 q^{96} - 170 q^{97} - 345 q^{98} - 480 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3610))\)

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
3610.2.a \(\chi_{3610}(1, \cdot)\) 3610.2.a.a 1 1
3610.2.a.b 1
3610.2.a.c 1
3610.2.a.d 1
3610.2.a.e 1
3610.2.a.f 1
3610.2.a.g 1
3610.2.a.h 1
3610.2.a.i 1
3610.2.a.j 2
3610.2.a.k 2
3610.2.a.l 2
3610.2.a.m 2
3610.2.a.n 2
3610.2.a.o 2
3610.2.a.p 2
3610.2.a.q 2
3610.2.a.r 2
3610.2.a.s 2
3610.2.a.t 2
3610.2.a.u 2
3610.2.a.v 2
3610.2.a.w 3
3610.2.a.x 3
3610.2.a.y 4
3610.2.a.z 4
3610.2.a.ba 4
3610.2.a.bb 4
3610.2.a.bc 6
3610.2.a.bd 6
3610.2.a.be 6
3610.2.a.bf 6
3610.2.a.bg 8
3610.2.a.bh 8
3610.2.a.bi 9
3610.2.a.bj 9
3610.2.b \(\chi_{3610}(2889, \cdot)\) n/a 170 1
3610.2.e \(\chi_{3610}(1151, \cdot)\) n/a 232 2
3610.2.f \(\chi_{3610}(1443, \cdot)\) n/a 340 2
3610.2.i \(\chi_{3610}(429, \cdot)\) n/a 340 2
3610.2.k \(\chi_{3610}(821, \cdot)\) n/a 672 6
3610.2.m \(\chi_{3610}(293, \cdot)\) n/a 680 4
3610.2.p \(\chi_{3610}(99, \cdot)\) n/a 1020 6
3610.2.q \(\chi_{3610}(191, \cdot)\) n/a 2232 18
3610.2.s \(\chi_{3610}(127, \cdot)\) n/a 2040 12
3610.2.v \(\chi_{3610}(39, \cdot)\) n/a 3420 18
3610.2.w \(\chi_{3610}(11, \cdot)\) n/a 4464 36
3610.2.y \(\chi_{3610}(37, \cdot)\) n/a 6840 36
3610.2.ba \(\chi_{3610}(49, \cdot)\) n/a 6840 36
3610.2.bc \(\chi_{3610}(61, \cdot)\) n/a 13824 108
3610.2.bd \(\chi_{3610}(27, \cdot)\) n/a 13680 72
3610.2.bf \(\chi_{3610}(9, \cdot)\) n/a 20520 108
3610.2.bi \(\chi_{3610}(3, \cdot)\) n/a 41040 216

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3610)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1805))\)\(^{\oplus 2}\)