↑

Properties

Label 2275.2
Level 2275
Weight 2
Dimension 173688
Nonzero newspaces 100
Sturm bound 806400
Trace bound 9

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2275 = 5^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(806400\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2275))\).

Total New Old
Modular forms 205632 178200 27432
Cusp forms 197569 173688 23881
Eisenstein series 8063 4512 3551

Trace form

\( 173688 q - 262 q^{2} - 256 q^{3} - 238 q^{4} - 308 q^{5} - 384 q^{6} - 306 q^{7} - 568 q^{8} - 186 q^{9} + O(q^{10}) \) \( 173688 q - 262 q^{2} - 256 q^{3} - 238 q^{4} - 308 q^{5} - 384 q^{6} - 306 q^{7} - 568 q^{8} - 186 q^{9} - 268 q^{10} - 372 q^{11} - 60 q^{12} - 230 q^{13} - 626 q^{14} - 728 q^{15} - 294 q^{16} - 194 q^{17} - 80 q^{18} - 200 q^{19} - 328 q^{20} - 440 q^{21} - 560 q^{22} - 192 q^{23} - 272 q^{24} - 372 q^{25} - 822 q^{26} - 544 q^{27} - 390 q^{28} - 618 q^{29} - 392 q^{30} - 388 q^{31} - 198 q^{32} - 228 q^{33} - 200 q^{34} - 416 q^{35} - 986 q^{36} - 182 q^{37} - 148 q^{38} - 264 q^{39} - 756 q^{40} - 290 q^{41} - 376 q^{42} - 576 q^{43} - 92 q^{44} - 460 q^{45} - 192 q^{46} - 116 q^{47} - 592 q^{48} - 122 q^{49} - 892 q^{50} - 700 q^{51} - 488 q^{52} - 544 q^{53} - 740 q^{54} - 440 q^{55} - 646 q^{56} - 1040 q^{57} - 686 q^{58} - 516 q^{59} - 1144 q^{60} - 610 q^{61} - 984 q^{62} - 750 q^{63} - 1500 q^{64} - 590 q^{65} - 1608 q^{66} - 688 q^{67} - 1102 q^{68} - 932 q^{69} - 828 q^{70} - 1084 q^{71} - 1602 q^{72} - 544 q^{73} - 822 q^{74} - 680 q^{75} - 1528 q^{76} - 588 q^{77} - 1144 q^{78} - 872 q^{79} - 748 q^{80} - 462 q^{81} - 598 q^{82} - 360 q^{83} - 976 q^{84} - 1004 q^{85} - 324 q^{86} - 296 q^{87} - 756 q^{88} - 432 q^{89} - 724 q^{90} - 632 q^{91} - 1584 q^{92} - 256 q^{93} - 512 q^{94} - 440 q^{95} - 436 q^{96} - 596 q^{97} - 682 q^{98} - 560 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2275))\)

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
2275.2.a \(\chi_{2275}(1, \cdot)\) 2275.2.a.a 1 1
2275.2.a.b 1
2275.2.a.c 1
2275.2.a.d 1
2275.2.a.e 1
2275.2.a.f 1
2275.2.a.g 1
2275.2.a.h 1
2275.2.a.i 2
2275.2.a.j 2
2275.2.a.k 2
2275.2.a.l 3
2275.2.a.m 3
2275.2.a.n 3
2275.2.a.o 4
2275.2.a.p 4
2275.2.a.q 5
2275.2.a.r 5
2275.2.a.s 6
2275.2.a.t 6
2275.2.a.u 6
2275.2.a.v 7
2275.2.a.w 7
2275.2.a.x 7
2275.2.a.y 7
2275.2.a.z 7
2275.2.a.ba 10
2275.2.a.bb 10
2275.2.c \(\chi_{2275}(274, \cdot)\) n/a 108 1
2275.2.d \(\chi_{2275}(701, \cdot)\) n/a 134 1
2275.2.f \(\chi_{2275}(974, \cdot)\) n/a 124 1
2275.2.i \(\chi_{2275}(1576, \cdot)\) n/a 264 2
2275.2.j \(\chi_{2275}(326, \cdot)\) n/a 304 2
2275.2.k \(\chi_{2275}(1101, \cdot)\) n/a 342 2
2275.2.l \(\chi_{2275}(926, \cdot)\) n/a 342 2
2275.2.m \(\chi_{2275}(1282, \cdot)\) n/a 252 2
2275.2.p \(\chi_{2275}(1126, \cdot)\) n/a 340 2
2275.2.r \(\chi_{2275}(118, \cdot)\) n/a 288 2
2275.2.s \(\chi_{2275}(818, \cdot)\) n/a 328 2
2275.2.u \(\chi_{2275}(174, \cdot)\) n/a 328 2
2275.2.x \(\chi_{2275}(57, \cdot)\) n/a 252 2
2275.2.y \(\chi_{2275}(456, \cdot)\) n/a 720 4
2275.2.ba \(\chi_{2275}(751, \cdot)\) n/a 342 2
2275.2.bb \(\chi_{2275}(74, \cdot)\) n/a 328 2
2275.2.bd \(\chi_{2275}(849, \cdot)\) n/a 328 2
2275.2.bi \(\chi_{2275}(324, \cdot)\) n/a 328 2
2275.2.bk \(\chi_{2275}(1499, \cdot)\) n/a 248 2
2275.2.bn \(\chi_{2275}(1374, \cdot)\) n/a 328 2
2275.2.bp \(\chi_{2275}(51, \cdot)\) n/a 344 2
2275.2.br \(\chi_{2275}(1226, \cdot)\) n/a 268 2
2275.2.bs \(\chi_{2275}(1849, \cdot)\) n/a 256 2
2275.2.bu \(\chi_{2275}(599, \cdot)\) n/a 288 2
2275.2.bw \(\chi_{2275}(576, \cdot)\) n/a 342 2
2275.2.ca \(\chi_{2275}(1024, \cdot)\) n/a 328 2
2275.2.cd \(\chi_{2275}(64, \cdot)\) n/a 848 4
2275.2.cf \(\chi_{2275}(246, \cdot)\) n/a 832 4
2275.2.cg \(\chi_{2275}(729, \cdot)\) n/a 720 4
2275.2.cj \(\chi_{2275}(93, \cdot)\) n/a 656 4
2275.2.cl \(\chi_{2275}(193, \cdot)\) n/a 656 4
2275.2.cm \(\chi_{2275}(1107, \cdot)\) n/a 504 4
2275.2.co \(\chi_{2275}(268, \cdot)\) n/a 656 4
2275.2.cq \(\chi_{2275}(201, \cdot)\) n/a 684 4
2275.2.ct \(\chi_{2275}(999, \cdot)\) n/a 656 4
2275.2.cv \(\chi_{2275}(349, \cdot)\) n/a 656 4
2275.2.cw \(\chi_{2275}(824, \cdot)\) n/a 656 4
2275.2.cz \(\chi_{2275}(257, \cdot)\) n/a 656 4
2275.2.da \(\chi_{2275}(68, \cdot)\) n/a 656 4
2275.2.dc \(\chi_{2275}(157, \cdot)\) n/a 576 4
2275.2.de \(\chi_{2275}(82, \cdot)\) n/a 656 4
2275.2.dh \(\chi_{2275}(1343, \cdot)\) n/a 656 4
2275.2.dj \(\chi_{2275}(243, \cdot)\) n/a 656 4
2275.2.dk \(\chi_{2275}(1693, \cdot)\) n/a 656 4
2275.2.dn \(\chi_{2275}(493, \cdot)\) n/a 656 4
2275.2.do \(\chi_{2275}(726, \cdot)\) n/a 684 4
2275.2.dr \(\chi_{2275}(551, \cdot)\) n/a 688 4
2275.2.ds \(\chi_{2275}(76, \cdot)\) n/a 688 4
2275.2.dv \(\chi_{2275}(24, \cdot)\) n/a 656 4
2275.2.dw \(\chi_{2275}(557, \cdot)\) n/a 656 4
2275.2.dz \(\chi_{2275}(18, \cdot)\) n/a 656 4
2275.2.eb \(\chi_{2275}(232, \cdot)\) n/a 504 4
2275.2.ec \(\chi_{2275}(32, \cdot)\) n/a 656 4
2275.2.ee \(\chi_{2275}(16, \cdot)\) n/a 2208 8
2275.2.ef \(\chi_{2275}(81, \cdot)\) n/a 2208 8
2275.2.eg \(\chi_{2275}(261, \cdot)\) n/a 1920 8
2275.2.eh \(\chi_{2275}(211, \cdot)\) n/a 1696 8
2275.2.ei \(\chi_{2275}(8, \cdot)\) n/a 1680 8
2275.2.el \(\chi_{2275}(34, \cdot)\) n/a 2208 8
2275.2.en \(\chi_{2275}(272, \cdot)\) n/a 2208 8
2275.2.eo \(\chi_{2275}(27, \cdot)\) n/a 1920 8
2275.2.eq \(\chi_{2275}(216, \cdot)\) n/a 2208 8
2275.2.et \(\chi_{2275}(148, \cdot)\) n/a 1680 8
2275.2.eu \(\chi_{2275}(4, \cdot)\) n/a 2208 8
2275.2.ey \(\chi_{2275}(121, \cdot)\) n/a 2208 8
2275.2.fa \(\chi_{2275}(79, \cdot)\) n/a 1920 8
2275.2.fc \(\chi_{2275}(29, \cdot)\) n/a 1664 8
2275.2.fd \(\chi_{2275}(36, \cdot)\) n/a 1664 8
2275.2.ff \(\chi_{2275}(116, \cdot)\) n/a 2208 8
2275.2.fh \(\chi_{2275}(9, \cdot)\) n/a 2208 8
2275.2.fk \(\chi_{2275}(134, \cdot)\) n/a 1696 8
2275.2.fm \(\chi_{2275}(389, \cdot)\) n/a 2208 8
2275.2.fr \(\chi_{2275}(179, \cdot)\) n/a 2208 8
2275.2.ft \(\chi_{2275}(289, \cdot)\) n/a 2208 8
2275.2.fu \(\chi_{2275}(186, \cdot)\) n/a 2208 8
2275.2.fx \(\chi_{2275}(2, \cdot)\) n/a 4416 16
2275.2.fy \(\chi_{2275}(177, \cdot)\) n/a 4416 16
2275.2.ga \(\chi_{2275}(253, \cdot)\) n/a 3360 16
2275.2.gd \(\chi_{2275}(58, \cdot)\) n/a 4416 16
2275.2.ge \(\chi_{2275}(19, \cdot)\) n/a 4416 16
2275.2.gh \(\chi_{2275}(6, \cdot)\) n/a 4416 16
2275.2.gi \(\chi_{2275}(31, \cdot)\) n/a 4416 16
2275.2.gl \(\chi_{2275}(136, \cdot)\) n/a 4416 16
2275.2.gm \(\chi_{2275}(12, \cdot)\) n/a 4416 16
2275.2.gp \(\chi_{2275}(48, \cdot)\) n/a 4416 16
2275.2.gq \(\chi_{2275}(3, \cdot)\) n/a 4416 16
2275.2.gs \(\chi_{2275}(62, \cdot)\) n/a 4416 16
2275.2.gv \(\chi_{2275}(173, \cdot)\) n/a 4416 16
2275.2.gx \(\chi_{2275}(222, \cdot)\) n/a 3840 16
2275.2.gz \(\chi_{2275}(87, \cdot)\) n/a 4416 16
2275.2.ha \(\chi_{2275}(17, \cdot)\) n/a 4416 16
2275.2.hd \(\chi_{2275}(164, \cdot)\) n/a 4416 16
2275.2.he \(\chi_{2275}(279, \cdot)\) n/a 4416 16
2275.2.hg \(\chi_{2275}(54, \cdot)\) n/a 4416 16
2275.2.hj \(\chi_{2275}(171, \cdot)\) n/a 4416 16
2275.2.hl \(\chi_{2275}(162, \cdot)\) n/a 3360 16
2275.2.hn \(\chi_{2275}(317, \cdot)\) n/a 4416 16
2275.2.ho \(\chi_{2275}(67, \cdot)\) n/a 4416 16
2275.2.hq \(\chi_{2275}(37, \cdot)\) n/a 4416 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2275)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(455))\)\(^{\oplus 2}\)