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Properties

Label 2975.2
Level 2975
Weight 2
Dimension 300058
Nonzero newspaces 72
Sturm bound 1382400
Trace bound 19

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Defining parameters

Level: \( N \) = \( 2975 = 5^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(1382400\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2975))\).

Total New Old
Modular forms 350976 306210 44766
Cusp forms 340225 300058 40167
Eisenstein series 10751 6152 4599

Trace form

\( 300058 q - 366 q^{2} - 360 q^{3} - 342 q^{4} - 436 q^{5} - 552 q^{6} - 438 q^{7} - 846 q^{8} - 306 q^{9} + O(q^{10}) \) \( 300058 q - 366 q^{2} - 360 q^{3} - 342 q^{4} - 436 q^{5} - 552 q^{6} - 438 q^{7} - 846 q^{8} - 306 q^{9} - 396 q^{10} - 536 q^{11} - 168 q^{12} - 284 q^{13} - 362 q^{14} - 1048 q^{15} - 430 q^{16} - 350 q^{17} - 602 q^{18} - 328 q^{19} - 456 q^{20} - 652 q^{21} - 848 q^{22} - 304 q^{23} - 416 q^{24} - 500 q^{25} - 1036 q^{26} - 360 q^{27} - 522 q^{28} - 892 q^{29} - 520 q^{30} - 544 q^{31} - 322 q^{32} - 336 q^{33} - 280 q^{34} - 1216 q^{35} - 1414 q^{36} - 256 q^{37} - 240 q^{38} - 352 q^{39} - 500 q^{40} - 460 q^{41} - 500 q^{42} - 848 q^{43} - 160 q^{44} - 588 q^{45} - 432 q^{46} - 224 q^{47} - 320 q^{48} - 278 q^{49} - 1188 q^{50} - 1088 q^{51} - 716 q^{52} - 152 q^{53} - 232 q^{54} - 424 q^{55} - 562 q^{56} - 776 q^{57} - 332 q^{58} - 288 q^{59} - 696 q^{60} - 572 q^{61} - 472 q^{62} - 522 q^{63} - 1478 q^{64} - 540 q^{65} - 512 q^{66} - 440 q^{67} - 566 q^{68} - 968 q^{69} - 972 q^{70} - 1592 q^{71} - 1278 q^{72} - 924 q^{73} - 1076 q^{74} - 824 q^{75} - 2152 q^{76} - 732 q^{77} - 1712 q^{78} - 832 q^{79} - 1348 q^{80} - 1050 q^{81} - 1460 q^{82} - 768 q^{83} - 1348 q^{84} - 1686 q^{85} - 1560 q^{86} - 1000 q^{87} - 1992 q^{88} - 824 q^{89} - 1396 q^{90} - 1000 q^{91} - 1960 q^{92} - 792 q^{93} - 1248 q^{94} - 824 q^{95} - 1448 q^{96} - 1028 q^{97} - 690 q^{98} - 1336 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2975))\)

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
2975.2.a \(\chi_{2975}(1, \cdot)\) 2975.2.a.a 1 1
2975.2.a.b 1
2975.2.a.c 1
2975.2.a.d 3
2975.2.a.e 3
2975.2.a.f 3
2975.2.a.g 3
2975.2.a.h 3
2975.2.a.i 4
2975.2.a.j 4
2975.2.a.k 4
2975.2.a.l 5
2975.2.a.m 5
2975.2.a.n 7
2975.2.a.o 7
2975.2.a.p 7
2975.2.a.q 7
2975.2.a.r 7
2975.2.a.s 7
2975.2.a.t 9
2975.2.a.u 9
2975.2.a.v 9
2975.2.a.w 9
2975.2.a.x 17
2975.2.a.y 17
2975.2.c \(\chi_{2975}(2024, \cdot)\) n/a 144 1
2975.2.d \(\chi_{2975}(2549, \cdot)\) n/a 164 1
2975.2.f \(\chi_{2975}(526, \cdot)\) n/a 170 1
2975.2.i \(\chi_{2975}(851, \cdot)\) n/a 404 2
2975.2.k \(\chi_{2975}(701, \cdot)\) n/a 340 2
2975.2.l \(\chi_{2975}(132, \cdot)\) n/a 424 2
2975.2.o \(\chi_{2975}(307, \cdot)\) n/a 384 2
2975.2.p \(\chi_{2975}(118, \cdot)\) n/a 424 2
2975.2.r \(\chi_{2975}(1007, \cdot)\) n/a 424 2
2975.2.t \(\chi_{2975}(1849, \cdot)\) n/a 328 2
2975.2.v \(\chi_{2975}(596, \cdot)\) n/a 960 4
2975.2.y \(\chi_{2975}(1376, \cdot)\) n/a 444 2
2975.2.ba \(\chi_{2975}(424, \cdot)\) n/a 424 2
2975.2.bb \(\chi_{2975}(324, \cdot)\) n/a 384 2
2975.2.be \(\chi_{2975}(468, \cdot)\) n/a 848 4
2975.2.bg \(\chi_{2975}(876, \cdot)\) n/a 688 4
2975.2.bh \(\chi_{2975}(274, \cdot)\) n/a 640 4
2975.2.bk \(\chi_{2975}(818, \cdot)\) n/a 848 4
2975.2.bn \(\chi_{2975}(1121, \cdot)\) n/a 1088 4
2975.2.bp \(\chi_{2975}(169, \cdot)\) n/a 1072 4
2975.2.bq \(\chi_{2975}(239, \cdot)\) n/a 960 4
2975.2.bs \(\chi_{2975}(149, \cdot)\) n/a 848 4
2975.2.bv \(\chi_{2975}(157, \cdot)\) n/a 848 4
2975.2.bw \(\chi_{2975}(1293, \cdot)\) n/a 768 4
2975.2.bz \(\chi_{2975}(1818, \cdot)\) n/a 848 4
2975.2.cb \(\chi_{2975}(1832, \cdot)\) n/a 848 4
2975.2.cd \(\chi_{2975}(676, \cdot)\) n/a 888 4
2975.2.ce \(\chi_{2975}(86, \cdot)\) n/a 2560 8
2975.2.cf \(\chi_{2975}(57, \cdot)\) n/a 1296 8
2975.2.ch \(\chi_{2975}(524, \cdot)\) n/a 1696 8
2975.2.ck \(\chi_{2975}(601, \cdot)\) n/a 1776 8
2975.2.cl \(\chi_{2975}(568, \cdot)\) n/a 1296 8
2975.2.co \(\chi_{2975}(64, \cdot)\) n/a 2144 8
2975.2.cq \(\chi_{2975}(13, \cdot)\) n/a 2848 8
2975.2.cs \(\chi_{2975}(237, \cdot)\) n/a 2848 8
2975.2.ct \(\chi_{2975}(188, \cdot)\) n/a 2560 8
2975.2.cw \(\chi_{2975}(727, \cdot)\) n/a 2848 8
2975.2.cx \(\chi_{2975}(106, \cdot)\) n/a 2176 8
2975.2.da \(\chi_{2975}(332, \cdot)\) n/a 1696 8
2975.2.db \(\chi_{2975}(151, \cdot)\) n/a 1776 8
2975.2.de \(\chi_{2975}(774, \cdot)\) n/a 1696 8
2975.2.dg \(\chi_{2975}(257, \cdot)\) n/a 1696 8
2975.2.di \(\chi_{2975}(494, \cdot)\) n/a 2560 8
2975.2.dj \(\chi_{2975}(254, \cdot)\) n/a 2848 8
2975.2.dl \(\chi_{2975}(16, \cdot)\) n/a 2848 8
2975.2.do \(\chi_{2975}(83, \cdot)\) n/a 5696 16
2975.2.dq \(\chi_{2975}(134, \cdot)\) n/a 4352 16
2975.2.dt \(\chi_{2975}(36, \cdot)\) n/a 4288 16
2975.2.du \(\chi_{2975}(202, \cdot)\) n/a 5696 16
2975.2.dw \(\chi_{2975}(282, \cdot)\) n/a 3392 16
2975.2.dy \(\chi_{2975}(201, \cdot)\) n/a 3552 16
2975.2.eb \(\chi_{2975}(24, \cdot)\) n/a 3392 16
2975.2.ec \(\chi_{2975}(107, \cdot)\) n/a 3392 16
2975.2.ee \(\chi_{2975}(81, \cdot)\) n/a 5696 16
2975.2.eg \(\chi_{2975}(38, \cdot)\) n/a 5696 16
2975.2.ei \(\chi_{2975}(33, \cdot)\) n/a 5696 16
2975.2.el \(\chi_{2975}(52, \cdot)\) n/a 5120 16
2975.2.em \(\chi_{2975}(327, \cdot)\) n/a 5696 16
2975.2.ep \(\chi_{2975}(4, \cdot)\) n/a 5696 16
2975.2.er \(\chi_{2975}(22, \cdot)\) n/a 8640 32
2975.2.et \(\chi_{2975}(139, \cdot)\) n/a 11392 32
2975.2.eu \(\chi_{2975}(6, \cdot)\) n/a 11392 32
2975.2.ex \(\chi_{2975}(92, \cdot)\) n/a 8640 32
2975.2.ey \(\chi_{2975}(87, \cdot)\) n/a 11392 32
2975.2.fb \(\chi_{2975}(9, \cdot)\) n/a 11392 32
2975.2.fc \(\chi_{2975}(121, \cdot)\) n/a 11392 32
2975.2.fe \(\chi_{2975}(138, \cdot)\) n/a 11392 32
2975.2.fh \(\chi_{2975}(23, \cdot)\) n/a 22784 64
2975.2.fj \(\chi_{2975}(31, \cdot)\) n/a 22784 64
2975.2.fk \(\chi_{2975}(54, \cdot)\) n/a 22784 64
2975.2.fn \(\chi_{2975}(88, \cdot)\) n/a 22784 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2975))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2975)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(595))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2975))\)\(^{\oplus 1}\)