# Properties

 Label 2925.2 Level 2925 Weight 2 Dimension 215991 Nonzero newspaces 100 Sturm bound 1209600 Trace bound 31

## Defining parameters

 Level: $$N$$ = $$2925 = 3^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$100$$ Sturm bound: $$1209600$$ Trace bound: $$31$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2925))$$.

Total New Old
Modular forms 307776 220049 87727
Cusp forms 297025 215991 81034
Eisenstein series 10751 4058 6693

## Trace form

 $$215991 q - 202 q^{2} - 264 q^{3} - 218 q^{4} - 246 q^{5} - 424 q^{6} - 224 q^{7} - 195 q^{8} - 248 q^{9} + O(q^{10})$$ $$215991 q - 202 q^{2} - 264 q^{3} - 218 q^{4} - 246 q^{5} - 424 q^{6} - 224 q^{7} - 195 q^{8} - 248 q^{9} - 714 q^{10} - 292 q^{11} - 200 q^{12} - 220 q^{13} - 372 q^{14} - 296 q^{15} - 286 q^{16} - 155 q^{17} - 168 q^{18} - 582 q^{19} - 108 q^{20} - 360 q^{21} - 92 q^{22} - 98 q^{23} - 64 q^{24} - 162 q^{25} - 636 q^{26} - 480 q^{27} - 388 q^{28} - 25 q^{29} - 240 q^{30} - 232 q^{31} + 26 q^{32} - 164 q^{33} - 20 q^{34} - 224 q^{35} - 392 q^{36} - 465 q^{37} - 52 q^{38} - 288 q^{39} - 462 q^{40} - 379 q^{41} - 304 q^{42} - 212 q^{43} - 192 q^{44} - 360 q^{45} - 838 q^{46} - 224 q^{47} - 400 q^{48} - 54 q^{49} - 98 q^{50} - 800 q^{51} + 27 q^{52} - 262 q^{53} - 248 q^{54} - 508 q^{55} + 24 q^{56} - 168 q^{57} + 211 q^{58} + 124 q^{59} - 424 q^{60} - 207 q^{61} + 178 q^{62} - 144 q^{63} - 317 q^{64} - 245 q^{65} - 632 q^{66} - 86 q^{67} - 65 q^{68} - 200 q^{69} - 444 q^{70} - 26 q^{71} - 540 q^{72} - 502 q^{73} - 413 q^{74} - 640 q^{75} - 406 q^{76} - 432 q^{77} - 324 q^{78} - 564 q^{79} - 1054 q^{80} - 584 q^{81} - 889 q^{82} - 640 q^{83} - 832 q^{84} - 330 q^{85} - 724 q^{86} - 512 q^{87} - 300 q^{88} - 540 q^{89} - 752 q^{90} - 1050 q^{91} - 736 q^{92} - 440 q^{93} + 130 q^{94} - 148 q^{95} - 932 q^{96} + 54 q^{97} - 370 q^{98} - 384 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2925))$$

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
2925.2.a $$\chi_{2925}(1, \cdot)$$ 2925.2.a.a 1 1
2925.2.a.b 1
2925.2.a.c 1
2925.2.a.d 1
2925.2.a.e 1
2925.2.a.f 1
2925.2.a.g 1
2925.2.a.h 1
2925.2.a.i 1
2925.2.a.j 1
2925.2.a.k 1
2925.2.a.l 1
2925.2.a.m 1
2925.2.a.n 1
2925.2.a.o 1
2925.2.a.p 1
2925.2.a.q 1
2925.2.a.r 1
2925.2.a.s 1
2925.2.a.t 1
2925.2.a.u 2
2925.2.a.v 2
2925.2.a.w 2
2925.2.a.x 2
2925.2.a.y 2
2925.2.a.z 2
2925.2.a.ba 2
2925.2.a.bb 2
2925.2.a.bc 2
2925.2.a.bd 2
2925.2.a.be 3
2925.2.a.bf 3
2925.2.a.bg 3
2925.2.a.bh 3
2925.2.a.bi 3
2925.2.a.bj 3
2925.2.a.bk 3
2925.2.a.bl 5
2925.2.a.bm 5
2925.2.a.bn 6
2925.2.a.bo 6
2925.2.a.bp 6
2925.2.a.bq 6
2925.2.b $$\chi_{2925}(1351, \cdot)$$ n/a 108 1
2925.2.c $$\chi_{2925}(2224, \cdot)$$ 2925.2.c.a 2 1
2925.2.c.b 2
2925.2.c.c 2
2925.2.c.d 2
2925.2.c.e 2
2925.2.c.f 2
2925.2.c.g 2
2925.2.c.h 2
2925.2.c.i 2
2925.2.c.j 2
2925.2.c.k 2
2925.2.c.l 2
2925.2.c.m 2
2925.2.c.n 2
2925.2.c.o 4
2925.2.c.p 4
2925.2.c.q 4
2925.2.c.r 4
2925.2.c.s 4
2925.2.c.t 4
2925.2.c.u 4
2925.2.c.v 4
2925.2.c.w 6
2925.2.c.x 6
2925.2.c.y 6
2925.2.c.z 12
2925.2.h $$\chi_{2925}(649, \cdot)$$ n/a 104 1
2925.2.i $$\chi_{2925}(976, \cdot)$$ n/a 456 2
2925.2.j $$\chi_{2925}(451, \cdot)$$ n/a 216 2
2925.2.k $$\chi_{2925}(2401, \cdot)$$ n/a 520 2
2925.2.l $$\chi_{2925}(601, \cdot)$$ n/a 520 2
2925.2.n $$\chi_{2925}(307, \cdot)$$ n/a 206 2
2925.2.p $$\chi_{2925}(1457, \cdot)$$ n/a 144 2
2925.2.q $$\chi_{2925}(1799, \cdot)$$ n/a 168 2
2925.2.r $$\chi_{2925}(476, \cdot)$$ n/a 180 2
2925.2.v $$\chi_{2925}(818, \cdot)$$ n/a 168 2
2925.2.w $$\chi_{2925}(1243, \cdot)$$ n/a 206 2
2925.2.y $$\chi_{2925}(586, \cdot)$$ n/a 600 4
2925.2.bb $$\chi_{2925}(1726, \cdot)$$ n/a 520 2
2925.2.bc $$\chi_{2925}(724, \cdot)$$ n/a 496 2
2925.2.bf $$\chi_{2925}(1624, \cdot)$$ n/a 496 2
2925.2.bg $$\chi_{2925}(199, \cdot)$$ n/a 208 2
2925.2.bl $$\chi_{2925}(49, \cdot)$$ n/a 496 2
2925.2.bm $$\chi_{2925}(1699, \cdot)$$ n/a 496 2
2925.2.bn $$\chi_{2925}(751, \cdot)$$ n/a 520 2
2925.2.bs $$\chi_{2925}(274, \cdot)$$ n/a 432 2
2925.2.bt $$\chi_{2925}(874, \cdot)$$ n/a 204 2
2925.2.bu $$\chi_{2925}(376, \cdot)$$ n/a 520 2
2925.2.bv $$\chi_{2925}(901, \cdot)$$ n/a 214 2
2925.2.by $$\chi_{2925}(1024, \cdot)$$ n/a 496 2
2925.2.cd $$\chi_{2925}(64, \cdot)$$ n/a 688 4
2925.2.ce $$\chi_{2925}(469, \cdot)$$ n/a 600 4
2925.2.cf $$\chi_{2925}(181, \cdot)$$ n/a 696 4
2925.2.ci $$\chi_{2925}(232, \cdot)$$ n/a 992 4
2925.2.ck $$\chi_{2925}(193, \cdot)$$ n/a 992 4
2925.2.cn $$\chi_{2925}(1432, \cdot)$$ n/a 412 4
2925.2.co $$\chi_{2925}(268, \cdot)$$ n/a 992 4
2925.2.cq $$\chi_{2925}(932, \cdot)$$ n/a 992 4
2925.2.cu $$\chi_{2925}(176, \cdot)$$ n/a 1040 4
2925.2.cv $$\chi_{2925}(149, \cdot)$$ n/a 992 4
2925.2.cw $$\chi_{2925}(218, \cdot)$$ n/a 992 4
2925.2.cz $$\chi_{2925}(257, \cdot)$$ n/a 992 4
2925.2.da $$\chi_{2925}(857, \cdot)$$ n/a 992 4
2925.2.dd $$\chi_{2925}(368, \cdot)$$ n/a 336 4
2925.2.de $$\chi_{2925}(1151, \cdot)$$ n/a 352 4
2925.2.df $$\chi_{2925}(449, \cdot)$$ n/a 336 4
2925.2.dk $$\chi_{2925}(749, \cdot)$$ n/a 992 4
2925.2.dl $$\chi_{2925}(401, \cdot)$$ n/a 1040 4
2925.2.dm $$\chi_{2925}(1424, \cdot)$$ n/a 992 4
2925.2.dn $$\chi_{2925}(551, \cdot)$$ n/a 1040 4
2925.2.dr $$\chi_{2925}(443, \cdot)$$ n/a 864 4
2925.2.ds $$\chi_{2925}(68, \cdot)$$ n/a 992 4
2925.2.dv $$\chi_{2925}(107, \cdot)$$ n/a 336 4
2925.2.dx $$\chi_{2925}(982, \cdot)$$ n/a 412 4
2925.2.dy $$\chi_{2925}(1282, \cdot)$$ n/a 992 4
2925.2.eb $$\chi_{2925}(7, \cdot)$$ n/a 992 4
2925.2.ed $$\chi_{2925}(457, \cdot)$$ n/a 992 4
2925.2.ee $$\chi_{2925}(16, \cdot)$$ n/a 3328 8
2925.2.ef $$\chi_{2925}(406, \cdot)$$ n/a 1376 8
2925.2.eg $$\chi_{2925}(196, \cdot)$$ n/a 2880 8
2925.2.eh $$\chi_{2925}(61, \cdot)$$ n/a 3328 8
2925.2.ei $$\chi_{2925}(73, \cdot)$$ n/a 1384 8
2925.2.ek $$\chi_{2925}(233, \cdot)$$ n/a 1120 8
2925.2.eo $$\chi_{2925}(161, \cdot)$$ n/a 1120 8
2925.2.ep $$\chi_{2925}(44, \cdot)$$ n/a 1120 8
2925.2.eq $$\chi_{2925}(53, \cdot)$$ n/a 960 8
2925.2.et $$\chi_{2925}(892, \cdot)$$ n/a 1384 8
2925.2.eu $$\chi_{2925}(4, \cdot)$$ n/a 3328 8
2925.2.ex $$\chi_{2925}(166, \cdot)$$ n/a 3328 8
2925.2.ey $$\chi_{2925}(94, \cdot)$$ n/a 3328 8
2925.2.fd $$\chi_{2925}(316, \cdot)$$ n/a 1392 8
2925.2.fe $$\chi_{2925}(571, \cdot)$$ n/a 3328 8
2925.2.ff $$\chi_{2925}(289, \cdot)$$ n/a 1392 8
2925.2.fg $$\chi_{2925}(79, \cdot)$$ n/a 2880 8
2925.2.fl $$\chi_{2925}(244, \cdot)$$ n/a 1376 8
2925.2.fm $$\chi_{2925}(259, \cdot)$$ n/a 3328 8
2925.2.fr $$\chi_{2925}(394, \cdot)$$ n/a 3328 8
2925.2.fu $$\chi_{2925}(139, \cdot)$$ n/a 3328 8
2925.2.fv $$\chi_{2925}(121, \cdot)$$ n/a 3328 8
2925.2.fx $$\chi_{2925}(292, \cdot)$$ n/a 6656 16
2925.2.fz $$\chi_{2925}(112, \cdot)$$ n/a 6656 16
2925.2.ga $$\chi_{2925}(28, \cdot)$$ n/a 2768 16
2925.2.gd $$\chi_{2925}(427, \cdot)$$ n/a 6656 16
2925.2.ge $$\chi_{2925}(152, \cdot)$$ n/a 2240 16
2925.2.gh $$\chi_{2925}(302, \cdot)$$ n/a 6656 16
2925.2.gi $$\chi_{2925}(92, \cdot)$$ n/a 5760 16
2925.2.gm $$\chi_{2925}(86, \cdot)$$ n/a 6656 16
2925.2.gn $$\chi_{2925}(254, \cdot)$$ n/a 6656 16
2925.2.go $$\chi_{2925}(41, \cdot)$$ n/a 6656 16
2925.2.gp $$\chi_{2925}(164, \cdot)$$ n/a 6656 16
2925.2.gu $$\chi_{2925}(89, \cdot)$$ n/a 2240 16
2925.2.gv $$\chi_{2925}(71, \cdot)$$ n/a 2240 16
2925.2.gw $$\chi_{2925}(17, \cdot)$$ n/a 2240 16
2925.2.gz $$\chi_{2925}(38, \cdot)$$ n/a 6656 16
2925.2.ha $$\chi_{2925}(23, \cdot)$$ n/a 6656 16
2925.2.hd $$\chi_{2925}(212, \cdot)$$ n/a 6656 16
2925.2.he $$\chi_{2925}(59, \cdot)$$ n/a 6656 16
2925.2.hf $$\chi_{2925}(11, \cdot)$$ n/a 6656 16
2925.2.hj $$\chi_{2925}(113, \cdot)$$ n/a 6656 16
2925.2.hk $$\chi_{2925}(67, \cdot)$$ n/a 6656 16
2925.2.hn $$\chi_{2925}(187, \cdot)$$ n/a 6656 16
2925.2.ho $$\chi_{2925}(163, \cdot)$$ n/a 2768 16
2925.2.hq $$\chi_{2925}(58, \cdot)$$ n/a 6656 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2925))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2925)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(975))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2925))$$$$^{\oplus 1}$$