# Properties

 Label 5915.2 Level 5915 Weight 2 Dimension 1176932 Nonzero newspaces 100 Sturm bound 5451264

## Defining parameters

 Level: $$N$$ = $$5915 = 5 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$100$$ Sturm bound: $$5451264$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5915))$$.

Total New Old
Modular forms 1373760 1189204 184556
Cusp forms 1351873 1176932 174941
Eisenstein series 21887 12272 9615

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5915))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
5915.2.a $$\chi_{5915}(1, \cdot)$$ 5915.2.a.a 1 1
5915.2.a.b 1
5915.2.a.c 1
5915.2.a.d 1
5915.2.a.e 1
5915.2.a.f 1
5915.2.a.g 1
5915.2.a.h 1
5915.2.a.i 1
5915.2.a.j 1
5915.2.a.k 1
5915.2.a.l 2
5915.2.a.m 4
5915.2.a.n 4
5915.2.a.o 5
5915.2.a.p 5
5915.2.a.q 5
5915.2.a.r 5
5915.2.a.s 5
5915.2.a.t 5
5915.2.a.u 6
5915.2.a.v 6
5915.2.a.w 6
5915.2.a.x 7
5915.2.a.y 7
5915.2.a.z 7
5915.2.a.ba 7
5915.2.a.bb 7
5915.2.a.bc 9
5915.2.a.bd 9
5915.2.a.be 10
5915.2.a.bf 10
5915.2.a.bg 15
5915.2.a.bh 15
5915.2.a.bi 15
5915.2.a.bj 15
5915.2.a.bk 15
5915.2.a.bl 15
5915.2.a.bm 18
5915.2.a.bn 18
5915.2.a.bo 21
5915.2.a.bp 21
5915.2.c $$\chi_{5915}(1184, \cdot)$$ n/a 466 1
5915.2.d $$\chi_{5915}(3886, \cdot)$$ n/a 308 1
5915.2.f $$\chi_{5915}(5069, \cdot)$$ n/a 460 1
5915.2.i $$\chi_{5915}(3571, \cdot)$$ n/a 616 2
5915.2.j $$\chi_{5915}(1691, \cdot)$$ n/a 828 2
5915.2.k $$\chi_{5915}(191, \cdot)$$ n/a 820 2
5915.2.l $$\chi_{5915}(1836, \cdot)$$ n/a 820 2
5915.2.m $$\chi_{5915}(1282, \cdot)$$ n/a 924 2
5915.2.p $$\chi_{5915}(5676, \cdot)$$ n/a 816 2
5915.2.r $$\chi_{5915}(3212, \cdot)$$ n/a 1196 2
5915.2.s $$\chi_{5915}(1182, \cdot)$$ n/a 1192 2
5915.2.u $$\chi_{5915}(944, \cdot)$$ n/a 1192 2
5915.2.x $$\chi_{5915}(1422, \cdot)$$ n/a 924 2
5915.2.z $$\chi_{5915}(1206, \cdot)$$ n/a 820 2
5915.2.ba $$\chi_{5915}(529, \cdot)$$ n/a 1192 2
5915.2.bc $$\chi_{5915}(1544, \cdot)$$ n/a 1192 2
5915.2.bh $$\chi_{5915}(844, \cdot)$$ n/a 1192 2
5915.2.bj $$\chi_{5915}(1499, \cdot)$$ n/a 920 2
5915.2.bm $$\chi_{5915}(1374, \cdot)$$ n/a 1192 2
5915.2.bo $$\chi_{5915}(506, \cdot)$$ n/a 824 2
5915.2.bq $$\chi_{5915}(316, \cdot)$$ n/a 616 2
5915.2.br $$\chi_{5915}(484, \cdot)$$ n/a 928 2
5915.2.bt $$\chi_{5915}(2874, \cdot)$$ n/a 1196 2
5915.2.bv $$\chi_{5915}(361, \cdot)$$ n/a 820 2
5915.2.bz $$\chi_{5915}(2389, \cdot)$$ n/a 1192 2
5915.2.cb $$\chi_{5915}(1033, \cdot)$$ n/a 2384 4
5915.2.cd $$\chi_{5915}(1103, \cdot)$$ n/a 2384 4
5915.2.ce $$\chi_{5915}(2178, \cdot)$$ n/a 1848 4
5915.2.cg $$\chi_{5915}(268, \cdot)$$ n/a 2384 4
5915.2.ci $$\chi_{5915}(1671, \cdot)$$ n/a 1640 4
5915.2.cl $$\chi_{5915}(89, \cdot)$$ n/a 2384 4
5915.2.cn $$\chi_{5915}(2554, \cdot)$$ n/a 2384 4
5915.2.co $$\chi_{5915}(4324, \cdot)$$ n/a 2384 4
5915.2.cr $$\chi_{5915}(1713, \cdot)$$ n/a 2384 4
5915.2.cs $$\chi_{5915}(1543, \cdot)$$ n/a 2384 4
5915.2.cu $$\chi_{5915}(677, \cdot)$$ n/a 2392 4
5915.2.cw $$\chi_{5915}(192, \cdot)$$ n/a 2384 4
5915.2.cz $$\chi_{5915}(1882, \cdot)$$ n/a 2384 4
5915.2.db $$\chi_{5915}(698, \cdot)$$ n/a 2384 4
5915.2.dc $$\chi_{5915}(867, \cdot)$$ n/a 2384 4
5915.2.df $$\chi_{5915}(1013, \cdot)$$ n/a 2384 4
5915.2.dg $$\chi_{5915}(1601, \cdot)$$ n/a 1640 4
5915.2.dj $$\chi_{5915}(3141, \cdot)$$ n/a 1648 4
5915.2.dk $$\chi_{5915}(1371, \cdot)$$ n/a 1648 4
5915.2.dn $$\chi_{5915}(19, \cdot)$$ n/a 2384 4
5915.2.do $$\chi_{5915}(1878, \cdot)$$ n/a 2384 4
5915.2.dr $$\chi_{5915}(408, \cdot)$$ n/a 2384 4
5915.2.dt $$\chi_{5915}(2108, \cdot)$$ n/a 1848 4
5915.2.du $$\chi_{5915}(1948, \cdot)$$ n/a 2384 4
5915.2.dw $$\chi_{5915}(456, \cdot)$$ n/a 4368 12
5915.2.dz $$\chi_{5915}(64, \cdot)$$ n/a 6576 12
5915.2.eb $$\chi_{5915}(246, \cdot)$$ n/a 4368 12
5915.2.ec $$\chi_{5915}(274, \cdot)$$ n/a 6528 12
5915.2.ee $$\chi_{5915}(16, \cdot)$$ n/a 11664 24
5915.2.ef $$\chi_{5915}(81, \cdot)$$ n/a 11664 24
5915.2.eg $$\chi_{5915}(261, \cdot)$$ n/a 11616 24
5915.2.eh $$\chi_{5915}(211, \cdot)$$ n/a 8736 24
5915.2.ei $$\chi_{5915}(8, \cdot)$$ n/a 13104 24
5915.2.ek $$\chi_{5915}(34, \cdot)$$ n/a 17376 24
5915.2.en $$\chi_{5915}(272, \cdot)$$ n/a 17376 24
5915.2.eo $$\chi_{5915}(27, \cdot)$$ n/a 17376 24
5915.2.er $$\chi_{5915}(216, \cdot)$$ n/a 11712 24
5915.2.et $$\chi_{5915}(148, \cdot)$$ n/a 13104 24
5915.2.eu $$\chi_{5915}(4, \cdot)$$ n/a 17376 24
5915.2.ey $$\chi_{5915}(121, \cdot)$$ n/a 11664 24
5915.2.fa $$\chi_{5915}(79, \cdot)$$ n/a 17376 24
5915.2.fc $$\chi_{5915}(29, \cdot)$$ n/a 13056 24
5915.2.fd $$\chi_{5915}(36, \cdot)$$ n/a 8736 24
5915.2.ff $$\chi_{5915}(51, \cdot)$$ n/a 11616 24
5915.2.fh $$\chi_{5915}(9, \cdot)$$ n/a 17376 24
5915.2.fk $$\chi_{5915}(134, \cdot)$$ n/a 13152 24
5915.2.fm $$\chi_{5915}(324, \cdot)$$ n/a 17376 24
5915.2.fr $$\chi_{5915}(179, \cdot)$$ n/a 17376 24
5915.2.ft $$\chi_{5915}(74, \cdot)$$ n/a 17376 24
5915.2.fu $$\chi_{5915}(186, \cdot)$$ n/a 11664 24
5915.2.fx $$\chi_{5915}(2, \cdot)$$ n/a 34752 48
5915.2.fy $$\chi_{5915}(232, \cdot)$$ n/a 26208 48
5915.2.ga $$\chi_{5915}(18, \cdot)$$ n/a 34752 48
5915.2.gd $$\chi_{5915}(58, \cdot)$$ n/a 34752 48
5915.2.gf $$\chi_{5915}(24, \cdot)$$ n/a 34752 48
5915.2.gg $$\chi_{5915}(6, \cdot)$$ n/a 23232 48
5915.2.gj $$\chi_{5915}(31, \cdot)$$ n/a 23232 48
5915.2.gk $$\chi_{5915}(136, \cdot)$$ n/a 23328 48
5915.2.gm $$\chi_{5915}(12, \cdot)$$ n/a 34752 48
5915.2.gp $$\chi_{5915}(48, \cdot)$$ n/a 34752 48
5915.2.gq $$\chi_{5915}(3, \cdot)$$ n/a 34752 48
5915.2.gs $$\chi_{5915}(62, \cdot)$$ n/a 34752 48
5915.2.gv $$\chi_{5915}(82, \cdot)$$ n/a 34752 48
5915.2.gx $$\chi_{5915}(157, \cdot)$$ n/a 34752 48
5915.2.gz $$\chi_{5915}(68, \cdot)$$ n/a 34752 48
5915.2.ha $$\chi_{5915}(17, \cdot)$$ n/a 34752 48
5915.2.hc $$\chi_{5915}(164, \cdot)$$ n/a 34752 48
5915.2.hf $$\chi_{5915}(279, \cdot)$$ n/a 34752 48
5915.2.hh $$\chi_{5915}(54, \cdot)$$ n/a 34752 48
5915.2.hi $$\chi_{5915}(171, \cdot)$$ n/a 23328 48
5915.2.hl $$\chi_{5915}(317, \cdot)$$ n/a 34752 48
5915.2.hn $$\chi_{5915}(162, \cdot)$$ n/a 26208 48
5915.2.ho $$\chi_{5915}(67, \cdot)$$ n/a 34752 48
5915.2.hq $$\chi_{5915}(37, \cdot)$$ n/a 34752 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5915))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5915)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(455))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(845))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1183))$$$$^{\oplus 2}$$