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Properties

Label 3680.2
Level 3680
Weight 2
Dimension 207036
Nonzero newspaces 40
Sturm bound 1622016
Trace bound 21

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Defining parameters

Level: \( N \) = \( 3680 = 2^{5} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(1622016\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3680))\).

Total New Old
Modular forms 411136 209556 201580
Cusp forms 399873 207036 192837
Eisenstein series 11263 2520 8743

Trace form

\( 207036 q - 160 q^{2} - 124 q^{3} - 160 q^{4} - 244 q^{5} - 480 q^{6} - 124 q^{7} - 160 q^{8} - 244 q^{9} + O(q^{10}) \) \( 207036 q - 160 q^{2} - 124 q^{3} - 160 q^{4} - 244 q^{5} - 480 q^{6} - 124 q^{7} - 160 q^{8} - 244 q^{9} - 224 q^{10} - 364 q^{11} - 96 q^{12} - 136 q^{13} - 96 q^{14} - 174 q^{15} - 400 q^{16} - 64 q^{17} - 80 q^{18} - 116 q^{19} - 208 q^{20} - 480 q^{21} - 112 q^{22} - 112 q^{23} - 384 q^{24} - 368 q^{25} - 560 q^{26} - 4 q^{27} - 240 q^{28} - 184 q^{29} - 304 q^{30} - 252 q^{31} - 240 q^{32} - 328 q^{33} - 208 q^{34} - 86 q^{35} - 592 q^{36} - 88 q^{37} - 128 q^{38} + 28 q^{39} - 216 q^{40} - 608 q^{41} - 80 q^{42} - 28 q^{43} - 124 q^{45} - 440 q^{46} - 192 q^{47} + 48 q^{48} - 36 q^{49} - 160 q^{50} - 348 q^{51} - 128 q^{52} - 24 q^{53} - 112 q^{54} - 206 q^{55} - 432 q^{56} - 280 q^{57} - 176 q^{58} - 244 q^{59} - 376 q^{60} - 392 q^{61} - 240 q^{62} - 332 q^{63} - 400 q^{64} - 684 q^{65} - 832 q^{66} - 332 q^{67} - 304 q^{68} - 200 q^{69} - 816 q^{70} - 556 q^{71} - 544 q^{72} - 384 q^{73} - 448 q^{74} - 358 q^{75} - 736 q^{76} - 288 q^{77} - 608 q^{78} - 228 q^{79} - 568 q^{80} - 452 q^{81} - 480 q^{82} - 44 q^{83} - 688 q^{84} - 400 q^{85} - 816 q^{86} + 12 q^{87} - 496 q^{88} - 320 q^{89} - 696 q^{90} - 192 q^{91} - 384 q^{92} - 576 q^{93} - 336 q^{94} - 70 q^{95} - 720 q^{96} - 384 q^{97} - 336 q^{98} + 92 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3680))\)

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
3680.2.a \(\chi_{3680}(1, \cdot)\) 3680.2.a.a 1 1
3680.2.a.b 1
3680.2.a.c 1
3680.2.a.d 1
3680.2.a.e 1
3680.2.a.f 1
3680.2.a.g 1
3680.2.a.h 1
3680.2.a.i 1
3680.2.a.j 1
3680.2.a.k 2
3680.2.a.l 2
3680.2.a.m 2
3680.2.a.n 2
3680.2.a.o 2
3680.2.a.p 2
3680.2.a.q 3
3680.2.a.r 3
3680.2.a.s 4
3680.2.a.t 4
3680.2.a.u 5
3680.2.a.v 5
3680.2.a.w 5
3680.2.a.x 5
3680.2.a.y 5
3680.2.a.z 5
3680.2.a.ba 5
3680.2.a.bb 5
3680.2.a.bc 6
3680.2.a.bd 6
3680.2.b \(\chi_{3680}(1839, \cdot)\) n/a 140 1
3680.2.e \(\chi_{3680}(2209, \cdot)\) n/a 132 1
3680.2.f \(\chi_{3680}(1841, \cdot)\) 3680.2.f.a 2 1
3680.2.f.b 8
3680.2.f.c 30
3680.2.f.d 48
3680.2.i \(\chi_{3680}(1471, \cdot)\) 3680.2.i.a 48 1
3680.2.i.b 48
3680.2.j \(\chi_{3680}(369, \cdot)\) n/a 132 1
3680.2.m \(\chi_{3680}(3679, \cdot)\) n/a 144 1
3680.2.n \(\chi_{3680}(3311, \cdot)\) 3680.2.n.a 48 1
3680.2.n.b 48
3680.2.r \(\chi_{3680}(873, \cdot)\) None 0 2
3680.2.t \(\chi_{3680}(1703, \cdot)\) None 0 2
3680.2.u \(\chi_{3680}(551, \cdot)\) None 0 2
3680.2.x \(\chi_{3680}(921, \cdot)\) None 0 2
3680.2.y \(\chi_{3680}(1057, \cdot)\) n/a 288 2
3680.2.ba \(\chi_{3680}(1887, \cdot)\) n/a 264 2
3680.2.bd \(\chi_{3680}(47, \cdot)\) n/a 264 2
3680.2.bf \(\chi_{3680}(2897, \cdot)\) n/a 280 2
3680.2.bg \(\chi_{3680}(1289, \cdot)\) None 0 2
3680.2.bj \(\chi_{3680}(919, \cdot)\) None 0 2
3680.2.bk \(\chi_{3680}(967, \cdot)\) None 0 2
3680.2.bm \(\chi_{3680}(137, \cdot)\) None 0 2
3680.2.bp \(\chi_{3680}(1243, \cdot)\) n/a 2112 4
3680.2.br \(\chi_{3680}(1333, \cdot)\) n/a 2288 4
3680.2.bs \(\chi_{3680}(459, \cdot)\) n/a 2288 4
3680.2.bu \(\chi_{3680}(461, \cdot)\) n/a 1408 4
3680.2.bx \(\chi_{3680}(91, \cdot)\) n/a 1536 4
3680.2.bz \(\chi_{3680}(829, \cdot)\) n/a 2112 4
3680.2.ca \(\chi_{3680}(323, \cdot)\) n/a 2112 4
3680.2.cc \(\chi_{3680}(413, \cdot)\) n/a 2288 4
3680.2.ce \(\chi_{3680}(961, \cdot)\) n/a 960 10
3680.2.ch \(\chi_{3680}(111, \cdot)\) n/a 960 10
3680.2.ci \(\chi_{3680}(159, \cdot)\) n/a 1440 10
3680.2.cl \(\chi_{3680}(49, \cdot)\) n/a 1400 10
3680.2.cm \(\chi_{3680}(191, \cdot)\) n/a 960 10
3680.2.cp \(\chi_{3680}(81, \cdot)\) n/a 960 10
3680.2.cq \(\chi_{3680}(289, \cdot)\) n/a 1440 10
3680.2.ct \(\chi_{3680}(79, \cdot)\) n/a 1400 10
3680.2.cv \(\chi_{3680}(153, \cdot)\) None 0 20
3680.2.cx \(\chi_{3680}(167, \cdot)\) None 0 20
3680.2.cz \(\chi_{3680}(199, \cdot)\) None 0 20
3680.2.da \(\chi_{3680}(9, \cdot)\) None 0 20
3680.2.dc \(\chi_{3680}(17, \cdot)\) n/a 2800 20
3680.2.de \(\chi_{3680}(303, \cdot)\) n/a 2800 20
3680.2.dh \(\chi_{3680}(127, \cdot)\) n/a 2880 20
3680.2.dj \(\chi_{3680}(33, \cdot)\) n/a 2880 20
3680.2.dl \(\chi_{3680}(41, \cdot)\) None 0 20
3680.2.dm \(\chi_{3680}(471, \cdot)\) None 0 20
3680.2.do \(\chi_{3680}(87, \cdot)\) None 0 20
3680.2.dq \(\chi_{3680}(57, \cdot)\) None 0 20
3680.2.dt \(\chi_{3680}(37, \cdot)\) n/a 22880 40
3680.2.dv \(\chi_{3680}(3, \cdot)\) n/a 22880 40
3680.2.dx \(\chi_{3680}(29, \cdot)\) n/a 22880 40
3680.2.dz \(\chi_{3680}(11, \cdot)\) n/a 15360 40
3680.2.ea \(\chi_{3680}(101, \cdot)\) n/a 15360 40
3680.2.ec \(\chi_{3680}(19, \cdot)\) n/a 22880 40
3680.2.ee \(\chi_{3680}(53, \cdot)\) n/a 22880 40
3680.2.eg \(\chi_{3680}(123, \cdot)\) n/a 22880 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3680))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3680)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(736))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1840))\)\(^{\oplus 2}\)