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Properties

Label 2640.2
Level 2640
Weight 2
Dimension 69608
Nonzero newspaces 56
Sturm bound 737280
Trace bound 26

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Defining parameters

Level: \( N \) = \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(737280\)
Trace bound: \(26\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2640))\).

Total New Old
Modular forms 188800 70576 118224
Cusp forms 179841 69608 110233
Eisenstein series 8959 968 7991

Trace form

\( 69608 q - 22 q^{3} - 80 q^{4} - 4 q^{5} - 120 q^{6} - 68 q^{7} - 48 q^{8} - 30 q^{9} + O(q^{10}) \) \( 69608 q - 22 q^{3} - 80 q^{4} - 4 q^{5} - 120 q^{6} - 68 q^{7} - 48 q^{8} - 30 q^{9} - 104 q^{10} - 24 q^{11} - 64 q^{12} - 116 q^{13} + 48 q^{14} - 77 q^{15} - 112 q^{16} - 24 q^{17} + 8 q^{18} - 140 q^{19} + 32 q^{20} - 136 q^{21} - 32 q^{22} - 16 q^{23} + 88 q^{24} - 26 q^{25} + 80 q^{26} + 2 q^{27} + 80 q^{28} - 24 q^{29} + 60 q^{30} - 36 q^{31} + 160 q^{32} - 102 q^{33} + 96 q^{34} + 36 q^{35} + 8 q^{36} - 116 q^{37} + 192 q^{38} - 14 q^{39} + 184 q^{40} - 56 q^{41} - 40 q^{42} - 72 q^{43} + 32 q^{44} - 166 q^{45} - 112 q^{46} - 72 q^{47} - 152 q^{48} - 328 q^{49} + 128 q^{50} + 14 q^{51} - 48 q^{52} + 8 q^{53} - 216 q^{54} - 86 q^{55} - 26 q^{57} + 16 q^{58} + 112 q^{59} - 92 q^{60} - 4 q^{61} - 48 q^{62} + 226 q^{63} + 112 q^{64} - 8 q^{65} - 64 q^{66} + 208 q^{67} - 96 q^{68} + 144 q^{69} + 48 q^{70} + 328 q^{71} - 40 q^{72} + 412 q^{73} + 256 q^{74} + 283 q^{75} + 464 q^{76} + 400 q^{77} + 272 q^{78} + 476 q^{79} + 136 q^{80} - 138 q^{81} + 592 q^{82} + 408 q^{83} + 120 q^{84} + 250 q^{85} + 320 q^{86} + 156 q^{87} + 976 q^{88} + 216 q^{89} - 252 q^{90} - 20 q^{91} + 288 q^{92} + 222 q^{93} + 528 q^{94} + 132 q^{95} - 40 q^{96} + 124 q^{97} + 624 q^{98} - 38 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2640))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2640.2.a \(\chi_{2640}(1, \cdot)\) 2640.2.a.a 1 1
2640.2.a.b 1
2640.2.a.c 1
2640.2.a.d 1
2640.2.a.e 1
2640.2.a.f 1
2640.2.a.g 1
2640.2.a.h 1
2640.2.a.i 1
2640.2.a.j 1
2640.2.a.k 1
2640.2.a.l 1
2640.2.a.m 1
2640.2.a.n 1
2640.2.a.o 1
2640.2.a.p 1
2640.2.a.q 1
2640.2.a.r 1
2640.2.a.s 1
2640.2.a.t 1
2640.2.a.u 1
2640.2.a.v 1
2640.2.a.w 1
2640.2.a.x 2
2640.2.a.y 2
2640.2.a.z 2
2640.2.a.ba 2
2640.2.a.bb 2
2640.2.a.bc 2
2640.2.a.bd 2
2640.2.a.be 3
2640.2.d \(\chi_{2640}(529, \cdot)\) 2640.2.d.a 2 1
2640.2.d.b 2
2640.2.d.c 4
2640.2.d.d 4
2640.2.d.e 4
2640.2.d.f 6
2640.2.d.g 6
2640.2.d.h 6
2640.2.d.i 6
2640.2.d.j 10
2640.2.d.k 10
2640.2.e \(\chi_{2640}(551, \cdot)\) None 0 1
2640.2.f \(\chi_{2640}(1121, \cdot)\) 2640.2.f.a 8 1
2640.2.f.b 8
2640.2.f.c 8
2640.2.f.d 8
2640.2.f.e 16
2640.2.f.f 24
2640.2.f.g 24
2640.2.g \(\chi_{2640}(439, \cdot)\) None 0 1
2640.2.j \(\chi_{2640}(1849, \cdot)\) None 0 1
2640.2.k \(\chi_{2640}(1871, \cdot)\) 2640.2.k.a 4 1
2640.2.k.b 4
2640.2.k.c 8
2640.2.k.d 8
2640.2.k.e 8
2640.2.k.f 8
2640.2.k.g 20
2640.2.k.h 20
2640.2.p \(\chi_{2640}(2441, \cdot)\) None 0 1
2640.2.q \(\chi_{2640}(1759, \cdot)\) 2640.2.q.a 12 1
2640.2.q.b 12
2640.2.q.c 24
2640.2.q.d 24
2640.2.t \(\chi_{2640}(1231, \cdot)\) 2640.2.t.a 4 1
2640.2.t.b 4
2640.2.t.c 8
2640.2.t.d 16
2640.2.t.e 16
2640.2.u \(\chi_{2640}(329, \cdot)\) None 0 1
2640.2.v \(\chi_{2640}(2399, \cdot)\) n/a 120 1
2640.2.w \(\chi_{2640}(1321, \cdot)\) None 0 1
2640.2.z \(\chi_{2640}(2551, \cdot)\) None 0 1
2640.2.ba \(\chi_{2640}(1649, \cdot)\) n/a 140 1
2640.2.bf \(\chi_{2640}(1079, \cdot)\) None 0 1
2640.2.bh \(\chi_{2640}(989, \cdot)\) n/a 1136 2
2640.2.bi \(\chi_{2640}(571, \cdot)\) n/a 384 2
2640.2.bl \(\chi_{2640}(661, \cdot)\) n/a 320 2
2640.2.bm \(\chi_{2640}(419, \cdot)\) n/a 960 2
2640.2.bo \(\chi_{2640}(1123, \cdot)\) n/a 480 2
2640.2.bq \(\chi_{2640}(923, \cdot)\) n/a 1136 2
2640.2.bt \(\chi_{2640}(2333, \cdot)\) n/a 960 2
2640.2.bv \(\chi_{2640}(373, \cdot)\) n/a 576 2
2640.2.bx \(\chi_{2640}(527, \cdot)\) n/a 288 2
2640.2.by \(\chi_{2640}(1033, \cdot)\) None 0 2
2640.2.cb \(\chi_{2640}(727, \cdot)\) None 0 2
2640.2.cc \(\chi_{2640}(353, \cdot)\) n/a 240 2
2640.2.cf \(\chi_{2640}(463, \cdot)\) n/a 120 2
2640.2.cg \(\chi_{2640}(617, \cdot)\) None 0 2
2640.2.cj \(\chi_{2640}(263, \cdot)\) None 0 2
2640.2.ck \(\chi_{2640}(1297, \cdot)\) n/a 144 2
2640.2.cm \(\chi_{2640}(2243, \cdot)\) n/a 1136 2
2640.2.co \(\chi_{2640}(67, \cdot)\) n/a 480 2
2640.2.cr \(\chi_{2640}(1693, \cdot)\) n/a 576 2
2640.2.ct \(\chi_{2640}(1013, \cdot)\) n/a 960 2
2640.2.cu \(\chi_{2640}(1211, \cdot)\) n/a 640 2
2640.2.cx \(\chi_{2640}(1189, \cdot)\) n/a 480 2
2640.2.cy \(\chi_{2640}(1099, \cdot)\) n/a 576 2
2640.2.db \(\chi_{2640}(461, \cdot)\) n/a 768 2
2640.2.dc \(\chi_{2640}(961, \cdot)\) n/a 192 4
2640.2.dd \(\chi_{2640}(119, \cdot)\) None 0 4
2640.2.di \(\chi_{2640}(151, \cdot)\) None 0 4
2640.2.dj \(\chi_{2640}(689, \cdot)\) n/a 560 4
2640.2.dm \(\chi_{2640}(719, \cdot)\) n/a 576 4
2640.2.dn \(\chi_{2640}(361, \cdot)\) None 0 4
2640.2.do \(\chi_{2640}(271, \cdot)\) n/a 192 4
2640.2.dp \(\chi_{2640}(569, \cdot)\) None 0 4
2640.2.ds \(\chi_{2640}(41, \cdot)\) None 0 4
2640.2.dt \(\chi_{2640}(79, \cdot)\) n/a 288 4
2640.2.dy \(\chi_{2640}(169, \cdot)\) None 0 4
2640.2.dz \(\chi_{2640}(191, \cdot)\) n/a 384 4
2640.2.ec \(\chi_{2640}(161, \cdot)\) n/a 384 4
2640.2.ed \(\chi_{2640}(679, \cdot)\) None 0 4
2640.2.ee \(\chi_{2640}(49, \cdot)\) n/a 288 4
2640.2.ef \(\chi_{2640}(71, \cdot)\) None 0 4
2640.2.ej \(\chi_{2640}(19, \cdot)\) n/a 2304 8
2640.2.ek \(\chi_{2640}(101, \cdot)\) n/a 3072 8
2640.2.en \(\chi_{2640}(251, \cdot)\) n/a 3072 8
2640.2.eo \(\chi_{2640}(229, \cdot)\) n/a 2304 8
2640.2.eq \(\chi_{2640}(53, \cdot)\) n/a 4544 8
2640.2.es \(\chi_{2640}(13, \cdot)\) n/a 2304 8
2640.2.ev \(\chi_{2640}(763, \cdot)\) n/a 2304 8
2640.2.ex \(\chi_{2640}(83, \cdot)\) n/a 4544 8
2640.2.ez \(\chi_{2640}(193, \cdot)\) n/a 576 8
2640.2.fa \(\chi_{2640}(167, \cdot)\) None 0 8
2640.2.fd \(\chi_{2640}(137, \cdot)\) None 0 8
2640.2.fe \(\chi_{2640}(223, \cdot)\) n/a 576 8
2640.2.fh \(\chi_{2640}(113, \cdot)\) n/a 1120 8
2640.2.fi \(\chi_{2640}(103, \cdot)\) None 0 8
2640.2.fl \(\chi_{2640}(73, \cdot)\) None 0 8
2640.2.fm \(\chi_{2640}(623, \cdot)\) n/a 1152 8
2640.2.fo \(\chi_{2640}(613, \cdot)\) n/a 2304 8
2640.2.fq \(\chi_{2640}(653, \cdot)\) n/a 4544 8
2640.2.ft \(\chi_{2640}(227, \cdot)\) n/a 4544 8
2640.2.fv \(\chi_{2640}(163, \cdot)\) n/a 2304 8
2640.2.fw \(\chi_{2640}(181, \cdot)\) n/a 1536 8
2640.2.fz \(\chi_{2640}(59, \cdot)\) n/a 4544 8
2640.2.ga \(\chi_{2640}(29, \cdot)\) n/a 4544 8
2640.2.gd \(\chi_{2640}(211, \cdot)\) n/a 1536 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2640))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2640)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2640))\)\(^{\oplus 1}\)