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Properties

Label 3960.1
Level 3960
Weight 1
Dimension 208
Nonzero newspaces 9
Newform subspaces 32
Sturm bound 829440
Trace bound 7

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Defining parameters

Level: \( N \) = \( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 32 \)
Sturm bound: \(829440\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3960))\).

Total New Old
Modular forms 8696 1180 7516
Cusp forms 1016 208 808
Eisenstein series 7680 972 6708

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 200 0 8 0

Trace form

\( 208 q - 14 q^{4} + 8 q^{7} - 8 q^{9} + O(q^{10}) \) \( 208 q - 14 q^{4} + 8 q^{7} - 8 q^{9} - 16 q^{10} - 2 q^{11} - 6 q^{14} - 4 q^{15} - 26 q^{16} + 4 q^{19} - 4 q^{20} - 4 q^{22} + 2 q^{25} + 8 q^{26} - 12 q^{28} + 20 q^{31} - 8 q^{34} + 4 q^{35} - 8 q^{40} - 6 q^{41} - 2 q^{44} - 16 q^{46} - 40 q^{49} + 20 q^{55} + 12 q^{56} - 12 q^{58} + 8 q^{59} + 22 q^{64} + 4 q^{65} - 16 q^{67} + 4 q^{69} - 2 q^{70} + 4 q^{71} + 12 q^{73} + 4 q^{74} + 4 q^{76} + 20 q^{79} + 8 q^{81} + 16 q^{82} - 4 q^{86} - 4 q^{88} - 34 q^{91} + 58 q^{94} + 8 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3960))\)

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
3960.1.b \(\chi_{3960}(1979, \cdot)\) 3960.1.b.a 4 1
3960.1.b.b 4
3960.1.b.c 8
3960.1.b.d 8
3960.1.c \(\chi_{3960}(2881, \cdot)\) None 0 1
3960.1.h \(\chi_{3960}(2971, \cdot)\) None 0 1
3960.1.i \(\chi_{3960}(89, \cdot)\) None 0 1
3960.1.l \(\chi_{3960}(3959, \cdot)\) None 0 1
3960.1.m \(\chi_{3960}(901, \cdot)\) None 0 1
3960.1.n \(\chi_{3960}(991, \cdot)\) None 0 1
3960.1.o \(\chi_{3960}(2069, \cdot)\) None 0 1
3960.1.r \(\chi_{3960}(2861, \cdot)\) None 0 1
3960.1.s \(\chi_{3960}(199, \cdot)\) None 0 1
3960.1.x \(\chi_{3960}(109, \cdot)\) 3960.1.x.a 1 1
3960.1.x.b 1
3960.1.x.c 1
3960.1.x.d 1
3960.1.x.e 2
3960.1.x.f 2
3960.1.x.g 2
3960.1.x.h 2
3960.1.x.i 4
3960.1.y \(\chi_{3960}(791, \cdot)\) None 0 1
3960.1.bb \(\chi_{3960}(881, \cdot)\) None 0 1
3960.1.bc \(\chi_{3960}(2179, \cdot)\) None 0 1
3960.1.bd \(\chi_{3960}(2089, \cdot)\) None 0 1
3960.1.be \(\chi_{3960}(2771, \cdot)\) None 0 1
3960.1.bh \(\chi_{3960}(683, \cdot)\) None 0 2
3960.1.bk \(\chi_{3960}(793, \cdot)\) None 0 2
3960.1.bl \(\chi_{3960}(703, \cdot)\) None 0 2
3960.1.bo \(\chi_{3960}(197, \cdot)\) None 0 2
3960.1.bp \(\chi_{3960}(307, \cdot)\) 3960.1.bp.a 8 2
3960.1.bp.b 8
3960.1.bs \(\chi_{3960}(593, \cdot)\) None 0 2
3960.1.bt \(\chi_{3960}(287, \cdot)\) None 0 2
3960.1.bw \(\chi_{3960}(397, \cdot)\) None 0 2
3960.1.ca \(\chi_{3960}(859, \cdot)\) None 0 2
3960.1.cb \(\chi_{3960}(2201, \cdot)\) None 0 2
3960.1.cc \(\chi_{3960}(131, \cdot)\) None 0 2
3960.1.cd \(\chi_{3960}(769, \cdot)\) 3960.1.cd.a 8 2
3960.1.cf \(\chi_{3960}(1519, \cdot)\) None 0 2
3960.1.cg \(\chi_{3960}(221, \cdot)\) None 0 2
3960.1.cl \(\chi_{3960}(2111, \cdot)\) None 0 2
3960.1.cm \(\chi_{3960}(1429, \cdot)\) 3960.1.cm.a 6 2
3960.1.cm.b 6
3960.1.cm.c 6
3960.1.cm.d 6
3960.1.cp \(\chi_{3960}(2221, \cdot)\) None 0 2
3960.1.cq \(\chi_{3960}(1319, \cdot)\) None 0 2
3960.1.cr \(\chi_{3960}(749, \cdot)\) None 0 2
3960.1.cs \(\chi_{3960}(2311, \cdot)\) None 0 2
3960.1.cv \(\chi_{3960}(241, \cdot)\) None 0 2
3960.1.cw \(\chi_{3960}(659, \cdot)\) None 0 2
3960.1.db \(\chi_{3960}(1409, \cdot)\) None 0 2
3960.1.dc \(\chi_{3960}(331, \cdot)\) None 0 2
3960.1.de \(\chi_{3960}(1009, \cdot)\) None 0 4
3960.1.df \(\chi_{3960}(611, \cdot)\) None 0 4
3960.1.dg \(\chi_{3960}(521, \cdot)\) None 0 4
3960.1.dh \(\chi_{3960}(379, \cdot)\) 3960.1.dh.a 4 4
3960.1.dh.b 4
3960.1.dh.c 8
3960.1.dh.d 8
3960.1.dk \(\chi_{3960}(469, \cdot)\) 3960.1.dk.a 8 4
3960.1.dk.b 8
3960.1.dk.c 8
3960.1.dk.d 8
3960.1.dl \(\chi_{3960}(431, \cdot)\) None 0 4
3960.1.dq \(\chi_{3960}(1061, \cdot)\) None 0 4
3960.1.dr \(\chi_{3960}(559, \cdot)\) None 0 4
3960.1.du \(\chi_{3960}(631, \cdot)\) None 0 4
3960.1.dv \(\chi_{3960}(269, \cdot)\) None 0 4
3960.1.dw \(\chi_{3960}(359, \cdot)\) None 0 4
3960.1.dx \(\chi_{3960}(541, \cdot)\) None 0 4
3960.1.ea \(\chi_{3960}(91, \cdot)\) None 0 4
3960.1.eb \(\chi_{3960}(449, \cdot)\) None 0 4
3960.1.eg \(\chi_{3960}(899, \cdot)\) 3960.1.eg.a 16 4
3960.1.eg.b 16
3960.1.eh \(\chi_{3960}(721, \cdot)\) None 0 4
3960.1.ei \(\chi_{3960}(1253, \cdot)\) None 0 4
3960.1.el \(\chi_{3960}(967, \cdot)\) None 0 4
3960.1.em \(\chi_{3960}(1057, \cdot)\) None 0 4
3960.1.ep \(\chi_{3960}(947, \cdot)\) None 0 4
3960.1.eq \(\chi_{3960}(133, \cdot)\) None 0 4
3960.1.et \(\chi_{3960}(23, \cdot)\) None 0 4
3960.1.eu \(\chi_{3960}(857, \cdot)\) None 0 4
3960.1.ex \(\chi_{3960}(43, \cdot)\) None 0 4
3960.1.ez \(\chi_{3960}(37, \cdot)\) 3960.1.ez.a 16 8
3960.1.ez.b 16
3960.1.fc \(\chi_{3960}(647, \cdot)\) None 0 8
3960.1.fd \(\chi_{3960}(17, \cdot)\) None 0 8
3960.1.fg \(\chi_{3960}(523, \cdot)\) None 0 8
3960.1.fh \(\chi_{3960}(413, \cdot)\) None 0 8
3960.1.fk \(\chi_{3960}(127, \cdot)\) None 0 8
3960.1.fl \(\chi_{3960}(433, \cdot)\) None 0 8
3960.1.fo \(\chi_{3960}(323, \cdot)\) None 0 8
3960.1.fp \(\chi_{3960}(929, \cdot)\) None 0 8
3960.1.fq \(\chi_{3960}(691, \cdot)\) None 0 8
3960.1.fv \(\chi_{3960}(481, \cdot)\) None 0 8
3960.1.fw \(\chi_{3960}(299, \cdot)\) None 0 8
3960.1.fz \(\chi_{3960}(389, \cdot)\) None 0 8
3960.1.ga \(\chi_{3960}(31, \cdot)\) None 0 8
3960.1.gb \(\chi_{3960}(61, \cdot)\) None 0 8
3960.1.gc \(\chi_{3960}(239, \cdot)\) None 0 8
3960.1.gf \(\chi_{3960}(1031, \cdot)\) None 0 8
3960.1.gg \(\chi_{3960}(349, \cdot)\) None 0 8
3960.1.gl \(\chi_{3960}(1039, \cdot)\) None 0 8
3960.1.gm \(\chi_{3960}(581, \cdot)\) None 0 8
3960.1.go \(\chi_{3960}(371, \cdot)\) None 0 8
3960.1.gp \(\chi_{3960}(409, \cdot)\) None 0 8
3960.1.gq \(\chi_{3960}(499, \cdot)\) None 0 8
3960.1.gr \(\chi_{3960}(401, \cdot)\) None 0 8
3960.1.gu \(\chi_{3960}(283, \cdot)\) None 0 16
3960.1.gx \(\chi_{3960}(497, \cdot)\) None 0 16
3960.1.gy \(\chi_{3960}(47, \cdot)\) None 0 16
3960.1.hb \(\chi_{3960}(157, \cdot)\) None 0 16
3960.1.hc \(\chi_{3960}(203, \cdot)\) None 0 16
3960.1.hf \(\chi_{3960}(97, \cdot)\) None 0 16
3960.1.hg \(\chi_{3960}(7, \cdot)\) None 0 16
3960.1.hj \(\chi_{3960}(173, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3960))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3960)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 32}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(990))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1980))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3960))\)\(^{\oplus 1}\)