Properties

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

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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

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