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Properties

Label 1860.2
Level 1860
Weight 2
Dimension 36532
Nonzero newspaces 48
Sturm bound 368640
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(368640\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1860))\).

Total New Old
Modular forms 94560 37236 57324
Cusp forms 89761 36532 53229
Eisenstein series 4799 704 4095

Trace form

\( 36532 q - 4 q^{3} - 44 q^{4} - 4 q^{5} - 74 q^{6} + 8 q^{7} + 24 q^{8} - 40 q^{9} + O(q^{10}) \) \( 36532 q - 4 q^{3} - 44 q^{4} - 4 q^{5} - 74 q^{6} + 8 q^{7} + 24 q^{8} - 40 q^{9} - 50 q^{10} + 16 q^{11} - 22 q^{12} - 72 q^{13} + 28 q^{15} - 180 q^{16} + 40 q^{17} - 62 q^{18} - 40 q^{20} - 166 q^{21} - 76 q^{22} - 60 q^{23} - 78 q^{24} - 172 q^{25} - 32 q^{26} - 28 q^{27} - 108 q^{28} - 144 q^{29} - 102 q^{30} - 144 q^{31} - 40 q^{32} - 144 q^{33} - 108 q^{34} - 92 q^{35} - 90 q^{36} - 300 q^{37} - 32 q^{38} - 70 q^{39} - 122 q^{40} - 52 q^{41} - 46 q^{42} + 4 q^{43} - 86 q^{45} - 132 q^{46} + 100 q^{48} + 36 q^{49} + 182 q^{50} + 204 q^{51} + 320 q^{52} + 112 q^{53} + 412 q^{54} + 136 q^{55} + 668 q^{56} + 80 q^{57} + 472 q^{58} + 136 q^{59} + 308 q^{60} + 192 q^{61} + 416 q^{62} + 224 q^{63} + 412 q^{64} + 140 q^{65} + 488 q^{66} + 128 q^{67} + 452 q^{68} + 56 q^{69} + 196 q^{70} + 240 q^{71} + 276 q^{72} - 96 q^{73} + 300 q^{74} + 101 q^{75} + 56 q^{76} + 24 q^{77} + 28 q^{78} - 48 q^{79} - 8 q^{80} - 112 q^{81} - 172 q^{82} - 142 q^{84} - 292 q^{85} - 128 q^{86} + 80 q^{87} - 268 q^{88} - 40 q^{89} - 165 q^{90} - 48 q^{91} - 112 q^{92} + 156 q^{93} - 328 q^{94} - 128 q^{96} - 56 q^{97} - 48 q^{98} + 134 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1860))\)

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
1860.2.a \(\chi_{1860}(1, \cdot)\) 1860.2.a.a 1 1
1860.2.a.b 1
1860.2.a.c 1
1860.2.a.d 2
1860.2.a.e 2
1860.2.a.f 3
1860.2.a.g 3
1860.2.a.h 3
1860.2.a.i 4
1860.2.f \(\chi_{1860}(991, \cdot)\) n/a 128 1
1860.2.g \(\chi_{1860}(1489, \cdot)\) 1860.2.g.a 14 1
1860.2.g.b 14
1860.2.h \(\chi_{1860}(311, \cdot)\) n/a 240 1
1860.2.i \(\chi_{1860}(929, \cdot)\) 1860.2.i.a 16 1
1860.2.i.b 48
1860.2.n \(\chi_{1860}(1799, \cdot)\) n/a 360 1
1860.2.o \(\chi_{1860}(1301, \cdot)\) 1860.2.o.a 44 1
1860.2.p \(\chi_{1860}(619, \cdot)\) n/a 192 1
1860.2.q \(\chi_{1860}(1141, \cdot)\) 1860.2.q.a 2 2
1860.2.q.b 2
1860.2.q.c 2
1860.2.q.d 2
1860.2.q.e 4
1860.2.q.f 6
1860.2.q.g 6
1860.2.q.h 8
1860.2.q.i 12
1860.2.r \(\chi_{1860}(497, \cdot)\) n/a 120 2
1860.2.s \(\chi_{1860}(433, \cdot)\) 1860.2.s.a 64 2
1860.2.t \(\chi_{1860}(743, \cdot)\) n/a 752 2
1860.2.u \(\chi_{1860}(187, \cdot)\) n/a 360 2
1860.2.z \(\chi_{1860}(481, \cdot)\) 1860.2.z.a 4 4
1860.2.z.b 16
1860.2.z.c 20
1860.2.z.d 20
1860.2.z.e 20
1860.2.ba \(\chi_{1860}(739, \cdot)\) n/a 384 2
1860.2.bb \(\chi_{1860}(161, \cdot)\) 1860.2.bb.a 4 2
1860.2.bb.b 80
1860.2.bc \(\chi_{1860}(1079, \cdot)\) n/a 752 2
1860.2.bh \(\chi_{1860}(1049, \cdot)\) n/a 128 2
1860.2.bi \(\chi_{1860}(191, \cdot)\) n/a 512 2
1860.2.bj \(\chi_{1860}(769, \cdot)\) 1860.2.bj.a 64 2
1860.2.bk \(\chi_{1860}(1111, \cdot)\) n/a 256 2
1860.2.bp \(\chi_{1860}(139, \cdot)\) n/a 768 4
1860.2.bq \(\chi_{1860}(401, \cdot)\) n/a 176 4
1860.2.br \(\chi_{1860}(419, \cdot)\) n/a 1504 4
1860.2.bw \(\chi_{1860}(29, \cdot)\) n/a 256 4
1860.2.bx \(\chi_{1860}(791, \cdot)\) n/a 1024 4
1860.2.by \(\chi_{1860}(109, \cdot)\) n/a 128 4
1860.2.bz \(\chi_{1860}(91, \cdot)\) n/a 512 4
1860.2.ci \(\chi_{1860}(67, \cdot)\) n/a 768 4
1860.2.cj \(\chi_{1860}(347, \cdot)\) n/a 1504 4
1860.2.ck \(\chi_{1860}(37, \cdot)\) n/a 128 4
1860.2.cl \(\chi_{1860}(377, \cdot)\) n/a 256 4
1860.2.cm \(\chi_{1860}(121, \cdot)\) n/a 176 8
1860.2.cr \(\chi_{1860}(163, \cdot)\) n/a 1536 8
1860.2.cs \(\chi_{1860}(23, \cdot)\) n/a 3008 8
1860.2.ct \(\chi_{1860}(277, \cdot)\) n/a 256 8
1860.2.cu \(\chi_{1860}(233, \cdot)\) n/a 512 8
1860.2.cz \(\chi_{1860}(331, \cdot)\) n/a 1024 8
1860.2.da \(\chi_{1860}(49, \cdot)\) n/a 256 8
1860.2.db \(\chi_{1860}(71, \cdot)\) n/a 2048 8
1860.2.dc \(\chi_{1860}(269, \cdot)\) n/a 512 8
1860.2.dh \(\chi_{1860}(59, \cdot)\) n/a 3008 8
1860.2.di \(\chi_{1860}(641, \cdot)\) n/a 336 8
1860.2.dj \(\chi_{1860}(79, \cdot)\) n/a 1536 8
1860.2.dk \(\chi_{1860}(113, \cdot)\) n/a 1024 16
1860.2.dl \(\chi_{1860}(13, \cdot)\) n/a 512 16
1860.2.dm \(\chi_{1860}(83, \cdot)\) n/a 6016 16
1860.2.dn \(\chi_{1860}(7, \cdot)\) n/a 3072 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1860))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1860)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(930))\)\(^{\oplus 2}\)