↑

Properties

Label 3913.1
Level 3913
Weight 1
Dimension 88
Nonzero newspaces 6
Newform subspaces 15
Sturm bound 1241856
Trace bound 9

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 3913 = 7 \cdot 13 \cdot 43 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 15 \)
Sturm bound: \(1241856\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3913))\).

Total New Old
Modular forms 6206 4600 1606
Cusp forms 158 88 70
Eisenstein series 6048 4512 1536

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 72 16 0 0

Trace form

\( 88 q + 4 q^{2} - 18 q^{4} + 8 q^{8} - 16 q^{9} + O(q^{10}) \) \( 88 q + 4 q^{2} - 18 q^{4} + 8 q^{8} - 16 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{14} - 10 q^{16} - 4 q^{17} + 4 q^{18} + 4 q^{22} - 22 q^{25} - 2 q^{29} + 38 q^{35} + 30 q^{36} - 4 q^{38} - 4 q^{40} + 4 q^{49} + 38 q^{53} + 8 q^{56} - 2 q^{58} + 46 q^{64} + 4 q^{66} + 8 q^{70} + 2 q^{72} + 4 q^{74} + 8 q^{78} + 4 q^{79} - 12 q^{81} - 8 q^{85} + 4 q^{86} - 4 q^{88} - 4 q^{91} - 4 q^{92} - 6 q^{95} + 2 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3913))\)

We only show spaces with odd 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
3913.1.b \(\chi_{3913}(3095, \cdot)\) None 0 1
3913.1.c \(\chi_{3913}(818, \cdot)\) None 0 1
3913.1.f \(\chi_{3913}(1119, \cdot)\) None 0 1
3913.1.g \(\chi_{3913}(2794, \cdot)\) None 0 1
3913.1.x \(\chi_{3913}(603, \cdot)\) None 0 2
3913.1.y \(\chi_{3913}(902, \cdot)\) None 0 2
3913.1.z \(\chi_{3913}(2200, \cdot)\) None 0 2
3913.1.ba \(\chi_{3913}(1382, \cdot)\) None 0 2
3913.1.bh \(\chi_{3913}(909, \cdot)\) 3913.1.bh.a 2 2
3913.1.bh.b 2
3913.1.bi \(\chi_{3913}(1076, \cdot)\) None 0 2
3913.1.bj \(\chi_{3913}(1167, \cdot)\) None 0 2
3913.1.bk \(\chi_{3913}(1985, \cdot)\) None 0 2
3913.1.bl \(\chi_{3913}(2622, \cdot)\) None 0 2
3913.1.bm \(\chi_{3913}(2458, \cdot)\) None 0 2
3913.1.bp \(\chi_{3913}(816, \cdot)\) None 0 2
3913.1.bq \(\chi_{3913}(480, \cdot)\) None 0 2
3913.1.br \(\chi_{3913}(953, \cdot)\) None 0 2
3913.1.bs \(\chi_{3913}(1511, \cdot)\) 3913.1.bs.a 4 2
3913.1.bt \(\chi_{3913}(1769, \cdot)\) None 0 2
3913.1.bu \(\chi_{3913}(2882, \cdot)\) None 0 2
3913.1.cb \(\chi_{3913}(2315, \cdot)\) None 0 2
3913.1.cc \(\chi_{3913}(1420, \cdot)\) None 0 2
3913.1.cd \(\chi_{3913}(3188, \cdot)\) None 0 2
3913.1.ce \(\chi_{3913}(179, \cdot)\) None 0 2
3913.1.cf \(\chi_{3913}(1117, \cdot)\) 3913.1.cf.a 2 2
3913.1.cf.b 2
3913.1.cf.c 4
3913.1.cf.d 4
3913.1.cf.e 4
3913.1.cf.f 8
3913.1.cf.g 16
3913.1.cg \(\chi_{3913}(1499, \cdot)\) None 0 2
3913.1.ch \(\chi_{3913}(2057, \cdot)\) 3913.1.ch.a 4 2
3913.1.ci \(\chi_{3913}(1678, \cdot)\) None 0 2
3913.1.cj \(\chi_{3913}(2973, \cdot)\) None 0 2
3913.1.ck \(\chi_{3913}(394, \cdot)\) None 0 2
3913.1.cl \(\chi_{3913}(1590, \cdot)\) None 0 2
3913.1.cm \(\chi_{3913}(1026, \cdot)\) None 0 2
3913.1.cq \(\chi_{3913}(173, \cdot)\) None 0 2
3913.1.cr \(\chi_{3913}(251, \cdot)\) None 0 2
3913.1.cs \(\chi_{3913}(1468, \cdot)\) None 0 2
3913.1.ct \(\chi_{3913}(781, \cdot)\) None 0 2
3913.1.cu \(\chi_{3913}(3305, \cdot)\) None 0 2
3913.1.cv \(\chi_{3913}(1719, \cdot)\) None 0 2
3913.1.di \(\chi_{3913}(386, \cdot)\) None 0 2
3913.1.dj \(\chi_{3913}(1327, \cdot)\) None 0 2
3913.1.dk \(\chi_{3913}(1628, \cdot)\) None 0 2
3913.1.dl \(\chi_{3913}(264, \cdot)\) None 0 2
3913.1.dm \(\chi_{3913}(1377, \cdot)\) None 0 2
3913.1.dn \(\chi_{3913}(1154, \cdot)\) None 0 2
3913.1.do \(\chi_{3913}(295, \cdot)\) None 0 2
3913.1.dp \(\chi_{3913}(1418, \cdot)\) None 0 2
3913.1.dq \(\chi_{3913}(1082, \cdot)\) None 0 2
3913.1.dr \(\chi_{3913}(810, \cdot)\) None 0 2
3913.1.ds \(\chi_{3913}(2014, \cdot)\) None 0 2
3913.1.dt \(\chi_{3913}(517, \cdot)\) None 0 2
3913.1.ea \(\chi_{3913}(178, \cdot)\) None 0 2
3913.1.eb \(\chi_{3913}(1297, \cdot)\) None 0 2
3913.1.ef \(\chi_{3913}(2157, \cdot)\) None 0 2
3913.1.eg \(\chi_{3913}(1843, \cdot)\) None 0 2
3913.1.eh \(\chi_{3913}(1934, \cdot)\) None 0 2
3913.1.ei \(\chi_{3913}(87, \cdot)\) None 0 2
3913.1.ej \(\chi_{3913}(724, \cdot)\) None 0 2
3913.1.ek \(\chi_{3913}(1210, \cdot)\) None 0 2
3913.1.ev \(\chi_{3913}(265, \cdot)\) None 0 4
3913.1.ew \(\chi_{3913}(136, \cdot)\) None 0 4
3913.1.ex \(\chi_{3913}(773, \cdot)\) None 0 4
3913.1.ey \(\chi_{3913}(947, \cdot)\) None 0 4
3913.1.ez \(\chi_{3913}(1038, \cdot)\) None 0 4
3913.1.fa \(\chi_{3913}(694, \cdot)\) None 0 4
3913.1.fb \(\chi_{3913}(80, \cdot)\) None 0 4
3913.1.fc \(\chi_{3913}(1203, \cdot)\) None 0 4
3913.1.fd \(\chi_{3913}(824, \cdot)\) None 0 4
3913.1.fe \(\chi_{3913}(1074, \cdot)\) None 0 4
3913.1.ff \(\chi_{3913}(1112, \cdot)\) None 0 4
3913.1.fg \(\chi_{3913}(1671, \cdot)\) None 0 4
3913.1.fh \(\chi_{3913}(681, \cdot)\) None 0 4
3913.1.fi \(\chi_{3913}(904, \cdot)\) None 0 4
3913.1.fj \(\chi_{3913}(522, \cdot)\) None 0 4
3913.1.fk \(\chi_{3913}(436, \cdot)\) None 0 4
3913.1.fl \(\chi_{3913}(995, \cdot)\) None 0 4
3913.1.fm \(\chi_{3913}(44, \cdot)\) None 0 4
3913.1.gf \(\chi_{3913}(1124, \cdot)\) None 0 4
3913.1.gg \(\chi_{3913}(682, \cdot)\) None 0 4
3913.1.gh \(\chi_{3913}(1541, \cdot)\) None 0 4
3913.1.gi \(\chi_{3913}(345, \cdot)\) None 0 4
3913.1.gj \(\chi_{3913}(135, \cdot)\) None 0 4
3913.1.gk \(\chi_{3913}(437, \cdot)\) None 0 4
3913.1.gl \(\chi_{3913}(171, \cdot)\) None 0 4
3913.1.gm \(\chi_{3913}(566, \cdot)\) None 0 4
3913.1.go \(\chi_{3913}(610, \cdot)\) None 0 6
3913.1.gp \(\chi_{3913}(391, \cdot)\) None 0 6
3913.1.gs \(\chi_{3913}(90, \cdot)\) 3913.1.gs.a 6 6
3913.1.gs.b 6
3913.1.gt \(\chi_{3913}(911, \cdot)\) None 0 6
3913.1.hh \(\chi_{3913}(125, \cdot)\) None 0 12
3913.1.hi \(\chi_{3913}(785, \cdot)\) None 0 12
3913.1.hm \(\chi_{3913}(482, \cdot)\) None 0 12
3913.1.hn \(\chi_{3913}(341, \cdot)\) None 0 12
3913.1.ho \(\chi_{3913}(250, \cdot)\) None 0 12
3913.1.hp \(\chi_{3913}(641, \cdot)\) None 0 12
3913.1.hq \(\chi_{3913}(205, \cdot)\) None 0 12
3913.1.hr \(\chi_{3913}(155, \cdot)\) None 0 12
3913.1.hv \(\chi_{3913}(114, \cdot)\) None 0 12
3913.1.hw \(\chi_{3913}(68, \cdot)\) None 0 12
3913.1.id \(\chi_{3913}(342, \cdot)\) None 0 12
3913.1.ie \(\chi_{3913}(38, \cdot)\) None 0 12
3913.1.if \(\chi_{3913}(10, \cdot)\) None 0 12
3913.1.ig \(\chi_{3913}(191, \cdot)\) None 0 12
3913.1.ih \(\chi_{3913}(352, \cdot)\) None 0 12
3913.1.ii \(\chi_{3913}(29, \cdot)\) None 0 12
3913.1.ij \(\chi_{3913}(160, \cdot)\) None 0 12
3913.1.ik \(\chi_{3913}(649, \cdot)\) None 0 12
3913.1.il \(\chi_{3913}(101, \cdot)\) None 0 12
3913.1.im \(\chi_{3913}(263, \cdot)\) None 0 12
3913.1.in \(\chi_{3913}(235, \cdot)\) None 0 12
3913.1.io \(\chi_{3913}(22, \cdot)\) None 0 12
3913.1.jb \(\chi_{3913}(555, \cdot)\) None 0 12
3913.1.jc \(\chi_{3913}(932, \cdot)\) None 0 12
3913.1.jd \(\chi_{3913}(261, \cdot)\) None 0 12
3913.1.je \(\chi_{3913}(402, \cdot)\) None 0 12
3913.1.jf \(\chi_{3913}(153, \cdot)\) None 0 12
3913.1.jg \(\chi_{3913}(355, \cdot)\) None 0 12
3913.1.jk \(\chi_{3913}(233, \cdot)\) None 0 12
3913.1.jl \(\chi_{3913}(309, \cdot)\) None 0 12
3913.1.jm \(\chi_{3913}(30, \cdot)\) None 0 12
3913.1.jn \(\chi_{3913}(152, \cdot)\) None 0 12
3913.1.jo \(\chi_{3913}(950, \cdot)\) None 0 12
3913.1.jp \(\chi_{3913}(139, \cdot)\) None 0 12
3913.1.jq \(\chi_{3913}(134, \cdot)\) None 0 12
3913.1.jr \(\chi_{3913}(51, \cdot)\) None 0 12
3913.1.js \(\chi_{3913}(485, \cdot)\) None 0 12
3913.1.jt \(\chi_{3913}(367, \cdot)\) None 0 12
3913.1.ju \(\chi_{3913}(594, \cdot)\) None 0 12
3913.1.jv \(\chi_{3913}(66, \cdot)\) None 0 12
3913.1.kc \(\chi_{3913}(1153, \cdot)\) None 0 12
3913.1.kd \(\chi_{3913}(40, \cdot)\) None 0 12
3913.1.ke \(\chi_{3913}(230, \cdot)\) None 0 12
3913.1.kf \(\chi_{3913}(218, \cdot)\) None 0 12
3913.1.kg \(\chi_{3913}(116, \cdot)\) None 0 12
3913.1.kh \(\chi_{3913}(88, \cdot)\) None 0 12
3913.1.kk \(\chi_{3913}(456, \cdot)\) None 0 12
3913.1.kl \(\chi_{3913}(438, \cdot)\) None 0 12
3913.1.km \(\chi_{3913}(562, \cdot)\) None 0 12
3913.1.kn \(\chi_{3913}(17, \cdot)\) None 0 12
3913.1.ko \(\chi_{3913}(348, \cdot)\) None 0 12
3913.1.kp \(\chi_{3913}(181, \cdot)\) 3913.1.kp.a 12 12
3913.1.kp.b 12
3913.1.kw \(\chi_{3913}(439, \cdot)\) None 0 12
3913.1.kx \(\chi_{3913}(198, \cdot)\) None 0 12
3913.1.ky \(\chi_{3913}(76, \cdot)\) None 0 24
3913.1.kz \(\chi_{3913}(297, \cdot)\) None 0 24
3913.1.la \(\chi_{3913}(5, \cdot)\) None 0 24
3913.1.lb \(\chi_{3913}(60, \cdot)\) None 0 24
3913.1.lc \(\chi_{3913}(11, \cdot)\) None 0 24
3913.1.ld \(\chi_{3913}(267, \cdot)\) None 0 24
3913.1.le \(\chi_{3913}(227, \cdot)\) None 0 24
3913.1.lf \(\chi_{3913}(275, \cdot)\) None 0 24
3913.1.ly \(\chi_{3913}(226, \cdot)\) None 0 24
3913.1.lz \(\chi_{3913}(15, \cdot)\) None 0 24
3913.1.ma \(\chi_{3913}(513, \cdot)\) None 0 24
3913.1.mb \(\chi_{3913}(58, \cdot)\) None 0 24
3913.1.mc \(\chi_{3913}(176, \cdot)\) None 0 24
3913.1.md \(\chi_{3913}(109, \cdot)\) None 0 24
3913.1.me \(\chi_{3913}(19, \cdot)\) None 0 24
3913.1.mf \(\chi_{3913}(20, \cdot)\) None 0 24
3913.1.mg \(\chi_{3913}(346, \cdot)\) None 0 24
3913.1.mh \(\chi_{3913}(304, \cdot)\) None 0 24
3913.1.mi \(\chi_{3913}(223, \cdot)\) None 0 24
3913.1.mj \(\chi_{3913}(201, \cdot)\) None 0 24
3913.1.mk \(\chi_{3913}(57, \cdot)\) None 0 24
3913.1.ml \(\chi_{3913}(228, \cdot)\) None 0 24
3913.1.mm \(\chi_{3913}(219, \cdot)\) None 0 24
3913.1.mn \(\chi_{3913}(45, \cdot)\) None 0 24
3913.1.mo \(\chi_{3913}(89, \cdot)\) None 0 24
3913.1.mp \(\chi_{3913}(34, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3913))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3913)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(301))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(559))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3913))\)\(^{\oplus 1}\)