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Properties

Label 3640.1
Level 3640
Weight 1
Dimension 360
Nonzero newspaces 19
Newform subspaces 72
Sturm bound 774144
Trace bound 16

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Defining parameters

Level: \( N \) = \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 19 \)
Newform subspaces: \( 72 \)
Sturm bound: \(774144\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3640))\).

Total New Old
Modular forms 7736 1680 6056
Cusp forms 824 360 464
Eisenstein series 6912 1320 5592

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 360 0 0 0

Trace form

\( 360 q + 20 q^{4} + 16 q^{9} + O(q^{10}) \) \( 360 q + 20 q^{4} + 16 q^{9} + 4 q^{10} - 4 q^{11} + 8 q^{15} - 20 q^{16} - 28 q^{19} - 12 q^{25} + 10 q^{26} + 34 q^{30} - 32 q^{35} - 52 q^{36} - 16 q^{39} + 4 q^{40} + 8 q^{41} + 36 q^{42} - 4 q^{44} - 4 q^{46} + 16 q^{49} - 16 q^{50} - 12 q^{51} - 8 q^{56} + 8 q^{59} + 64 q^{60} - 48 q^{63} - 28 q^{64} - 6 q^{65} + 48 q^{72} + 44 q^{74} - 12 q^{75} - 16 q^{76} - 8 q^{79} - 16 q^{89} + 28 q^{90} + 4 q^{91} + 44 q^{94} - 8 q^{95} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3640))\)

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
3640.1.c \(\chi_{3640}(2339, \cdot)\) None 0 1
3640.1.e \(\chi_{3640}(2001, \cdot)\) None 0 1
3640.1.f \(\chi_{3640}(911, \cdot)\) None 0 1
3640.1.h \(\chi_{3640}(2029, \cdot)\) None 0 1
3640.1.k \(\chi_{3640}(3121, \cdot)\) None 0 1
3640.1.m \(\chi_{3640}(3459, \cdot)\) None 0 1
3640.1.n \(\chi_{3640}(909, \cdot)\) 3640.1.n.a 1 1
3640.1.n.b 1
3640.1.n.c 1
3640.1.n.d 1
3640.1.n.e 2
3640.1.n.f 2
3640.1.n.g 8
3640.1.n.h 8
3640.1.p \(\chi_{3640}(3431, \cdot)\) None 0 1
3640.1.s \(\chi_{3640}(1639, \cdot)\) None 0 1
3640.1.u \(\chi_{3640}(1301, \cdot)\) None 0 1
3640.1.v \(\chi_{3640}(1611, \cdot)\) None 0 1
3640.1.x \(\chi_{3640}(2729, \cdot)\) None 0 1
3640.1.ba \(\chi_{3640}(181, \cdot)\) None 0 1
3640.1.bc \(\chi_{3640}(519, \cdot)\) None 0 1
3640.1.bd \(\chi_{3640}(209, \cdot)\) None 0 1
3640.1.bf \(\chi_{3640}(2731, \cdot)\) None 0 1
3640.1.bk \(\chi_{3640}(421, \cdot)\) None 0 2
3640.1.bl \(\chi_{3640}(1399, \cdot)\) None 0 2
3640.1.bq \(\chi_{3640}(811, \cdot)\) None 0 2
3640.1.br \(\chi_{3640}(1009, \cdot)\) None 0 2
3640.1.bs \(\chi_{3640}(1847, \cdot)\) None 0 2
3640.1.bv \(\chi_{3640}(363, \cdot)\) 3640.1.bv.a 4 2
3640.1.bv.b 4
3640.1.bv.c 8
3640.1.bv.d 8
3640.1.bw \(\chi_{3640}(337, \cdot)\) None 0 2
3640.1.bz \(\chi_{3640}(1093, \cdot)\) None 0 2
3640.1.cb \(\chi_{3640}(2673, \cdot)\) None 0 2
3640.1.cc \(\chi_{3640}(2423, \cdot)\) None 0 2
3640.1.cf \(\chi_{3640}(463, \cdot)\) None 0 2
3640.1.cg \(\chi_{3640}(993, \cdot)\) None 0 2
3640.1.ci \(\chi_{3640}(603, \cdot)\) None 0 2
3640.1.cl \(\chi_{3640}(853, \cdot)\) 3640.1.cl.a 2 2
3640.1.cl.b 2
3640.1.cl.c 2
3640.1.cl.d 2
3640.1.cl.e 4
3640.1.cl.f 4
3640.1.cm \(\chi_{3640}(2813, \cdot)\) 3640.1.cm.a 2 2
3640.1.cm.b 2
3640.1.cm.c 2
3640.1.cm.d 2
3640.1.cm.e 4
3640.1.cm.f 4
3640.1.cp \(\chi_{3640}(2283, \cdot)\) None 0 2
3640.1.cr \(\chi_{3640}(1457, \cdot)\) None 0 2
3640.1.cs \(\chi_{3640}(2157, \cdot)\) None 0 2
3640.1.cv \(\chi_{3640}(727, \cdot)\) None 0 2
3640.1.cw \(\chi_{3640}(27, \cdot)\) None 0 2
3640.1.cy \(\chi_{3640}(1539, \cdot)\) 3640.1.cy.a 4 2
3640.1.cy.b 4
3640.1.cz \(\chi_{3640}(281, \cdot)\) None 0 2
3640.1.de \(\chi_{3640}(1149, \cdot)\) None 0 2
3640.1.df \(\chi_{3640}(671, \cdot)\) None 0 2
3640.1.dh \(\chi_{3640}(191, \cdot)\) None 0 2
3640.1.dj \(\chi_{3640}(549, \cdot)\) None 0 2
3640.1.dk \(\chi_{3640}(179, \cdot)\) 3640.1.dk.a 4 2
3640.1.dk.b 4
3640.1.dm \(\chi_{3640}(1921, \cdot)\) None 0 2
3640.1.dp \(\chi_{3640}(829, \cdot)\) None 0 2
3640.1.dr \(\chi_{3640}(1031, \cdot)\) None 0 2
3640.1.ds \(\chi_{3640}(1641, \cdot)\) None 0 2
3640.1.du \(\chi_{3640}(2739, \cdot)\) 3640.1.du.a 2 2
3640.1.du.b 2
3640.1.du.c 2
3640.1.du.d 2
3640.1.dx \(\chi_{3640}(1479, \cdot)\) None 0 2
3640.1.dz \(\chi_{3640}(381, \cdot)\) None 0 2
3640.1.ea \(\chi_{3640}(1171, \cdot)\) None 0 2
3640.1.eb \(\chi_{3640}(211, \cdot)\) None 0 2
3640.1.ee \(\chi_{3640}(1049, \cdot)\) None 0 2
3640.1.ef \(\chi_{3640}(1249, \cdot)\) None 0 2
3640.1.eg \(\chi_{3640}(3039, \cdot)\) None 0 2
3640.1.eh \(\chi_{3640}(2599, \cdot)\) None 0 2
3640.1.ek \(\chi_{3640}(1221, \cdot)\) None 0 2
3640.1.el \(\chi_{3640}(2701, \cdot)\) None 0 2
3640.1.eo \(\chi_{3640}(2291, \cdot)\) None 0 2
3640.1.ep \(\chi_{3640}(2089, \cdot)\) None 0 2
3640.1.es \(\chi_{3640}(341, \cdot)\) None 0 2
3640.1.eu \(\chi_{3640}(1199, \cdot)\) None 0 2
3640.1.ex \(\chi_{3640}(1609, \cdot)\) None 0 2
3640.1.ey \(\chi_{3640}(129, \cdot)\) None 0 2
3640.1.fb \(\chi_{3640}(51, \cdot)\) None 0 2
3640.1.fc \(\chi_{3640}(491, \cdot)\) None 0 2
3640.1.fd \(\chi_{3640}(2341, \cdot)\) None 0 2
3640.1.fe \(\chi_{3640}(2141, \cdot)\) None 0 2
3640.1.fh \(\chi_{3640}(2479, \cdot)\) None 0 2
3640.1.fi \(\chi_{3640}(79, \cdot)\) None 0 2
3640.1.fl \(\chi_{3640}(2929, \cdot)\) None 0 2
3640.1.fn \(\chi_{3640}(2571, \cdot)\) None 0 2
3640.1.fq \(\chi_{3640}(3019, \cdot)\) 3640.1.fq.a 2 2
3640.1.fq.b 2
3640.1.fq.c 2
3640.1.fq.d 2
3640.1.fs \(\chi_{3640}(1361, \cdot)\) None 0 2
3640.1.fv \(\chi_{3640}(2311, \cdot)\) None 0 2
3640.1.fw \(\chi_{3640}(1871, \cdot)\) None 0 2
3640.1.fz \(\chi_{3640}(1949, \cdot)\) None 0 2
3640.1.ga \(\chi_{3640}(69, \cdot)\) 3640.1.ga.a 2 2
3640.1.ga.b 2
3640.1.ga.c 2
3640.1.ga.d 2
3640.1.ga.e 4
3640.1.ga.f 4
3640.1.gb \(\chi_{3640}(1899, \cdot)\) None 0 2
3640.1.gc \(\chi_{3640}(659, \cdot)\) None 0 2
3640.1.gf \(\chi_{3640}(321, \cdot)\) None 0 2
3640.1.gg \(\chi_{3640}(521, \cdot)\) None 0 2
3640.1.gj \(\chi_{3640}(751, \cdot)\) None 0 2
3640.1.gl \(\chi_{3640}(1109, \cdot)\) None 0 2
3640.1.go \(\chi_{3640}(2201, \cdot)\) None 0 2
3640.1.gq \(\chi_{3640}(459, \cdot)\) 3640.1.gq.a 4 2
3640.1.gq.b 4
3640.1.gt \(\chi_{3640}(3069, \cdot)\) None 0 2
3640.1.gu \(\chi_{3640}(2869, \cdot)\) 3640.1.gu.a 8 2
3640.1.gu.b 8
3640.1.gx \(\chi_{3640}(1751, \cdot)\) None 0 2
3640.1.gy \(\chi_{3640}(2991, \cdot)\) None 0 2
3640.1.gz \(\chi_{3640}(881, \cdot)\) None 0 2
3640.1.ha \(\chi_{3640}(3041, \cdot)\) None 0 2
3640.1.hd \(\chi_{3640}(779, \cdot)\) 3640.1.hd.a 4 2
3640.1.hd.b 4
3640.1.hd.c 12
3640.1.hd.d 12
3640.1.he \(\chi_{3640}(1219, \cdot)\) None 0 2
3640.1.hh \(\chi_{3640}(269, \cdot)\) None 0 2
3640.1.hj \(\chi_{3640}(471, \cdot)\) None 0 2
3640.1.hm \(\chi_{3640}(2851, \cdot)\) None 0 2
3640.1.ho \(\chi_{3640}(2649, \cdot)\) None 0 2
3640.1.hp \(\chi_{3640}(919, \cdot)\) None 0 2
3640.1.hr \(\chi_{3640}(61, \cdot)\) None 0 2
3640.1.hu \(\chi_{3640}(2369, \cdot)\) None 0 2
3640.1.hv \(\chi_{3640}(2011, \cdot)\) None 0 2
3640.1.hw \(\chi_{3640}(101, \cdot)\) None 0 2
3640.1.hy \(\chi_{3640}(1759, \cdot)\) None 0 2
3640.1.ia \(\chi_{3640}(249, \cdot)\) None 0 4
3640.1.ib \(\chi_{3640}(171, \cdot)\) None 0 4
3640.1.ig \(\chi_{3640}(479, \cdot)\) None 0 4
3640.1.ih \(\chi_{3640}(1341, \cdot)\) None 0 4
3640.1.ii \(\chi_{3640}(401, \cdot)\) None 0 4
3640.1.ij \(\chi_{3640}(59, \cdot)\) 3640.1.ij.a 8 4
3640.1.ij.b 8
3640.1.im \(\chi_{3640}(109, \cdot)\) None 0 4
3640.1.in \(\chi_{3640}(111, \cdot)\) None 0 4
3640.1.io \(\chi_{3640}(869, \cdot)\) None 0 4
3640.1.ip \(\chi_{3640}(31, \cdot)\) None 0 4
3640.1.iy \(\chi_{3640}(619, \cdot)\) 3640.1.iy.a 8 4
3640.1.iy.b 8
3640.1.iz \(\chi_{3640}(561, \cdot)\) None 0 4
3640.1.ja \(\chi_{3640}(1259, \cdot)\) 3640.1.ja.a 8 4
3640.1.ja.b 8
3640.1.jb \(\chi_{3640}(681, \cdot)\) None 0 4
3640.1.je \(\chi_{3640}(271, \cdot)\) None 0 4
3640.1.jf \(\chi_{3640}(669, \cdot)\) None 0 4
3640.1.jg \(\chi_{3640}(283, \cdot)\) None 0 4
3640.1.jj \(\chi_{3640}(367, \cdot)\) None 0 4
3640.1.jk \(\chi_{3640}(373, \cdot)\) None 0 4
3640.1.jn \(\chi_{3640}(1577, \cdot)\) None 0 4
3640.1.jo \(\chi_{3640}(717, \cdot)\) None 0 4
3640.1.jr \(\chi_{3640}(1467, \cdot)\) None 0 4
3640.1.js \(\chi_{3640}(67, \cdot)\) None 0 4
3640.1.jv \(\chi_{3640}(397, \cdot)\) None 0 4
3640.1.jx \(\chi_{3640}(527, \cdot)\) None 0 4
3640.1.jy \(\chi_{3640}(33, \cdot)\) None 0 4
3640.1.kb \(\chi_{3640}(297, \cdot)\) None 0 4
3640.1.kc \(\chi_{3640}(1103, \cdot)\) None 0 4
3640.1.kf \(\chi_{3640}(1213, \cdot)\) None 0 4
3640.1.kg \(\chi_{3640}(737, \cdot)\) None 0 4
3640.1.kj \(\chi_{3640}(3, \cdot)\) None 0 4
3640.1.kk \(\chi_{3640}(647, \cdot)\) None 0 4
3640.1.kn \(\chi_{3640}(103, \cdot)\) None 0 4
3640.1.kp \(\chi_{3640}(523, \cdot)\) None 0 4
3640.1.kr \(\chi_{3640}(867, \cdot)\) None 0 4
3640.1.ks \(\chi_{3640}(1063, \cdot)\) None 0 4
3640.1.ku \(\chi_{3640}(927, \cdot)\) None 0 4
3640.1.kw \(\chi_{3640}(1067, \cdot)\) None 0 4
3640.1.kz \(\chi_{3640}(417, \cdot)\) None 0 4
3640.1.lb \(\chi_{3640}(1037, \cdot)\) None 0 4
3640.1.ld \(\chi_{3640}(277, \cdot)\) None 0 4
3640.1.le \(\chi_{3640}(1017, \cdot)\) None 0 4
3640.1.lg \(\chi_{3640}(113, \cdot)\) None 0 4
3640.1.li \(\chi_{3640}(597, \cdot)\) None 0 4
3640.1.ll \(\chi_{3640}(2033, \cdot)\) None 0 4
3640.1.lm \(\chi_{3640}(2543, \cdot)\) None 0 4
3640.1.lp \(\chi_{3640}(863, \cdot)\) None 0 4
3640.1.lq \(\chi_{3640}(73, \cdot)\) None 0 4
3640.1.lt \(\chi_{3640}(773, \cdot)\) None 0 4
3640.1.lv \(\chi_{3640}(323, \cdot)\) None 0 4
3640.1.lw \(\chi_{3640}(1077, \cdot)\) 3640.1.lw.a 4 4
3640.1.lw.b 4
3640.1.lw.c 4
3640.1.lw.d 4
3640.1.lw.e 8
3640.1.lw.f 8
3640.1.ly \(\chi_{3640}(683, \cdot)\) None 0 4
3640.1.mb \(\chi_{3640}(123, \cdot)\) None 0 4
3640.1.md \(\chi_{3640}(293, \cdot)\) 3640.1.md.a 4 4
3640.1.md.b 4
3640.1.md.c 4
3640.1.md.d 4
3640.1.md.e 8
3640.1.md.f 8
3640.1.me \(\chi_{3640}(267, \cdot)\) None 0 4
3640.1.mg \(\chi_{3640}(453, \cdot)\) None 0 4
3640.1.mi \(\chi_{3640}(487, \cdot)\) None 0 4
3640.1.mk \(\chi_{3640}(657, \cdot)\) None 0 4
3640.1.mn \(\chi_{3640}(1527, \cdot)\) None 0 4
3640.1.mp \(\chi_{3640}(817, \cdot)\) None 0 4
3640.1.mq \(\chi_{3640}(1137, \cdot)\) None 0 4
3640.1.ms \(\chi_{3640}(687, \cdot)\) None 0 4
3640.1.mv \(\chi_{3640}(97, \cdot)\) None 0 4
3640.1.mx \(\chi_{3640}(1047, \cdot)\) None 0 4
3640.1.my \(\chi_{3640}(723, \cdot)\) None 0 4
3640.1.nb \(\chi_{3640}(213, \cdot)\) None 0 4
3640.1.nc \(\chi_{3640}(1893, \cdot)\) None 0 4
3640.1.nf \(\chi_{3640}(2683, \cdot)\) None 0 4
3640.1.ng \(\chi_{3640}(233, \cdot)\) None 0 4
3640.1.ni \(\chi_{3640}(653, \cdot)\) None 0 4
3640.1.nk \(\chi_{3640}(477, \cdot)\) None 0 4
3640.1.nn \(\chi_{3640}(673, \cdot)\) None 0 4
3640.1.np \(\chi_{3640}(1297, \cdot)\) None 0 4
3640.1.nr \(\chi_{3640}(53, \cdot)\) None 0 4
3640.1.ns \(\chi_{3640}(703, \cdot)\) None 0 4
3640.1.nu \(\chi_{3640}(1427, \cdot)\) None 0 4
3640.1.nw \(\chi_{3640}(563, \cdot)\) None 0 4
3640.1.nz \(\chi_{3640}(87, \cdot)\) None 0 4
3640.1.ob \(\chi_{3640}(503, \cdot)\) None 0 4
3640.1.od \(\chi_{3640}(467, \cdot)\) 3640.1.od.a 24 4
3640.1.od.b 24
3640.1.oe \(\chi_{3640}(999, \cdot)\) None 0 4
3640.1.of \(\chi_{3640}(501, \cdot)\) None 0 4
3640.1.oi \(\chi_{3640}(411, \cdot)\) None 0 4
3640.1.oj \(\chi_{3640}(449, \cdot)\) None 0 4
3640.1.ok \(\chi_{3640}(531, \cdot)\) None 0 4
3640.1.ol \(\chi_{3640}(1409, \cdot)\) None 0 4
3640.1.ou \(\chi_{3640}(541, \cdot)\) None 0 4
3640.1.ov \(\chi_{3640}(279, \cdot)\) None 0 4
3640.1.ow \(\chi_{3640}(141, \cdot)\) None 0 4
3640.1.ox \(\chi_{3640}(759, \cdot)\) None 0 4
3640.1.pa \(\chi_{3640}(1129, \cdot)\) None 0 4
3640.1.pb \(\chi_{3640}(691, \cdot)\) None 0 4
3640.1.pc \(\chi_{3640}(1111, \cdot)\) None 0 4
3640.1.pd \(\chi_{3640}(149, \cdot)\) None 0 4
3640.1.pi \(\chi_{3640}(921, \cdot)\) None 0 4
3640.1.pj \(\chi_{3640}(19, \cdot)\) 3640.1.pj.a 8 4
3640.1.pj.b 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3640))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3640)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(455))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(910))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1820))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3640))\)\(^{\oplus 1}\)