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Properties

Label 3700.2
Level 3700
Weight 2
Dimension 218889
Nonzero newspaces 60
Sturm bound 1641600
Trace bound 7

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Defining parameters

Level: \( N \) = \( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1641600\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3700))\).

Total New Old
Modular forms 415440 221761 193679
Cusp forms 405361 218889 186472
Eisenstein series 10079 2872 7207

Trace form

\( 218889 q - 222 q^{2} - 8 q^{3} - 214 q^{4} - 546 q^{5} - 342 q^{6} + 8 q^{7} - 198 q^{8} - 424 q^{9} + O(q^{10}) \) \( 218889 q - 222 q^{2} - 8 q^{3} - 214 q^{4} - 546 q^{5} - 342 q^{6} + 8 q^{7} - 198 q^{8} - 424 q^{9} - 256 q^{10} - 214 q^{12} - 428 q^{13} - 214 q^{14} + 4 q^{15} - 374 q^{16} - 408 q^{17} - 238 q^{18} + 24 q^{19} - 276 q^{20} - 660 q^{21} - 214 q^{22} + 64 q^{23} - 234 q^{24} - 462 q^{25} - 666 q^{26} + 52 q^{27} - 214 q^{28} - 382 q^{29} - 268 q^{30} - 30 q^{31} - 182 q^{32} - 424 q^{33} - 214 q^{34} + 16 q^{35} - 340 q^{36} - 519 q^{37} - 508 q^{38} - 138 q^{39} - 376 q^{40} - 818 q^{41} - 414 q^{42} - 156 q^{43} - 354 q^{44} - 686 q^{45} - 462 q^{46} - 122 q^{47} - 474 q^{48} - 594 q^{49} - 476 q^{50} - 72 q^{51} - 410 q^{52} - 470 q^{53} - 474 q^{54} - 80 q^{55} - 462 q^{56} - 556 q^{57} - 304 q^{58} + 24 q^{59} - 468 q^{60} - 535 q^{61} - 224 q^{62} + 136 q^{63} - 148 q^{64} - 446 q^{65} - 186 q^{66} + 124 q^{67} - 154 q^{68} - 192 q^{69} - 268 q^{70} + 104 q^{71} + 50 q^{72} - 320 q^{73} - 90 q^{74} + 156 q^{75} - 474 q^{76} - 196 q^{77} - 22 q^{78} + 184 q^{79} - 236 q^{80} - 720 q^{81} + 38 q^{82} + 160 q^{83} + 198 q^{84} - 630 q^{85} - 96 q^{86} + 80 q^{87} + 116 q^{88} - 577 q^{89} + 44 q^{90} + 6 q^{91} + 4 q^{92} - 670 q^{93} + 106 q^{94} - 72 q^{95} - 142 q^{96} - 828 q^{97} + 82 q^{98} - 210 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3700))\)

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
3700.2.a \(\chi_{3700}(1, \cdot)\) 3700.2.a.a 1 1
3700.2.a.b 1
3700.2.a.c 1
3700.2.a.d 1
3700.2.a.e 1
3700.2.a.f 1
3700.2.a.g 2
3700.2.a.h 2
3700.2.a.i 3
3700.2.a.j 4
3700.2.a.k 5
3700.2.a.l 5
3700.2.a.m 6
3700.2.a.n 6
3700.2.a.o 9
3700.2.a.p 9
3700.2.d \(\chi_{3700}(149, \cdot)\) 3700.2.d.a 2 1
3700.2.d.b 2
3700.2.d.c 2
3700.2.d.d 2
3700.2.d.e 2
3700.2.d.f 4
3700.2.d.g 4
3700.2.d.h 6
3700.2.d.i 8
3700.2.d.j 10
3700.2.d.k 12
3700.2.e \(\chi_{3700}(1849, \cdot)\) 3700.2.e.a 2 1
3700.2.e.b 2
3700.2.e.c 4
3700.2.e.d 4
3700.2.e.e 12
3700.2.e.f 12
3700.2.e.g 20
3700.2.h \(\chi_{3700}(1701, \cdot)\) 3700.2.h.a 2 1
3700.2.h.b 2
3700.2.h.c 2
3700.2.h.d 2
3700.2.h.e 10
3700.2.h.f 10
3700.2.h.g 12
3700.2.h.h 20
3700.2.i \(\chi_{3700}(1601, \cdot)\) n/a 118 2
3700.2.k \(\chi_{3700}(2399, \cdot)\) n/a 676 2
3700.2.l \(\chi_{3700}(1893, \cdot)\) n/a 114 2
3700.2.m \(\chi_{3700}(443, \cdot)\) n/a 676 2
3700.2.n \(\chi_{3700}(1407, \cdot)\) n/a 648 2
3700.2.o \(\chi_{3700}(857, \cdot)\) n/a 114 2
3700.2.u \(\chi_{3700}(2251, \cdot)\) n/a 710 2
3700.2.v \(\chi_{3700}(741, \cdot)\) n/a 360 4
3700.2.y \(\chi_{3700}(101, \cdot)\) n/a 120 2
3700.2.bb \(\chi_{3700}(249, \cdot)\) n/a 112 2
3700.2.bc \(\chi_{3700}(1749, \cdot)\) n/a 116 2
3700.2.bd \(\chi_{3700}(201, \cdot)\) n/a 360 6
3700.2.be \(\chi_{3700}(221, \cdot)\) n/a 376 4
3700.2.bh \(\chi_{3700}(369, \cdot)\) n/a 384 4
3700.2.bi \(\chi_{3700}(889, \cdot)\) n/a 360 4
3700.2.bm \(\chi_{3700}(51, \cdot)\) n/a 1420 4
3700.2.bn \(\chi_{3700}(2493, \cdot)\) n/a 228 4
3700.2.bo \(\chi_{3700}(343, \cdot)\) n/a 1352 4
3700.2.bp \(\chi_{3700}(307, \cdot)\) n/a 1352 4
3700.2.bq \(\chi_{3700}(193, \cdot)\) n/a 228 4
3700.2.bw \(\chi_{3700}(199, \cdot)\) n/a 1352 4
3700.2.bx \(\chi_{3700}(121, \cdot)\) n/a 768 8
3700.2.by \(\chi_{3700}(1249, \cdot)\) n/a 336 6
3700.2.bz \(\chi_{3700}(1101, \cdot)\) n/a 366 6
3700.2.ca \(\chi_{3700}(49, \cdot)\) n/a 348 6
3700.2.cf \(\chi_{3700}(31, \cdot)\) n/a 4528 8
3700.2.cl \(\chi_{3700}(117, \cdot)\) n/a 760 8
3700.2.cm \(\chi_{3700}(223, \cdot)\) n/a 4320 8
3700.2.cn \(\chi_{3700}(147, \cdot)\) n/a 4528 8
3700.2.co \(\chi_{3700}(413, \cdot)\) n/a 760 8
3700.2.cp \(\chi_{3700}(179, \cdot)\) n/a 4528 8
3700.2.cr \(\chi_{3700}(269, \cdot)\) n/a 752 8
3700.2.cs \(\chi_{3700}(529, \cdot)\) n/a 768 8
3700.2.cv \(\chi_{3700}(381, \cdot)\) n/a 752 8
3700.2.cz \(\chi_{3700}(351, \cdot)\) n/a 4260 12
3700.2.dc \(\chi_{3700}(499, \cdot)\) n/a 4056 12
3700.2.de \(\chi_{3700}(257, \cdot)\) n/a 684 12
3700.2.dg \(\chi_{3700}(243, \cdot)\) n/a 4056 12
3700.2.dh \(\chi_{3700}(7, \cdot)\) n/a 4056 12
3700.2.dj \(\chi_{3700}(57, \cdot)\) n/a 684 12
3700.2.dk \(\chi_{3700}(81, \cdot)\) n/a 2304 24
3700.2.dl \(\chi_{3700}(119, \cdot)\) n/a 9056 16
3700.2.dr \(\chi_{3700}(177, \cdot)\) n/a 1520 16
3700.2.ds \(\chi_{3700}(27, \cdot)\) n/a 9056 16
3700.2.dt \(\chi_{3700}(47, \cdot)\) n/a 9056 16
3700.2.du \(\chi_{3700}(97, \cdot)\) n/a 1520 16
3700.2.dv \(\chi_{3700}(171, \cdot)\) n/a 9056 16
3700.2.eb \(\chi_{3700}(9, \cdot)\) n/a 2256 24
3700.2.ec \(\chi_{3700}(21, \cdot)\) n/a 2256 24
3700.2.ed \(\chi_{3700}(169, \cdot)\) n/a 2304 24
3700.2.ee \(\chi_{3700}(13, \cdot)\) n/a 4560 48
3700.2.eg \(\chi_{3700}(83, \cdot)\) n/a 27168 48
3700.2.eh \(\chi_{3700}(3, \cdot)\) n/a 27168 48
3700.2.ej \(\chi_{3700}(17, \cdot)\) n/a 4560 48
3700.2.el \(\chi_{3700}(19, \cdot)\) n/a 27168 48
3700.2.eo \(\chi_{3700}(91, \cdot)\) n/a 27168 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3700))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3700)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(740))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(925))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3700))\)\(^{\oplus 1}\)