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Properties

Label 2760.2
Level 2760
Weight 2
Dimension 77608
Nonzero newspaces 36
Sturm bound 811008
Trace bound 20

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Defining parameters

Level: \( N \) = \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(811008\)
Trace bound: \(20\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2760))\).

Total New Old
Modular forms 206976 78616 128360
Cusp forms 198529 77608 120921
Eisenstein series 8447 1008 7439

Trace form

\( 77608 q - 8 q^{2} - 48 q^{3} - 88 q^{4} - 8 q^{5} - 108 q^{6} - 104 q^{7} + 16 q^{8} - 88 q^{9} + O(q^{10}) \) \( 77608 q - 8 q^{2} - 48 q^{3} - 88 q^{4} - 8 q^{5} - 108 q^{6} - 104 q^{7} + 16 q^{8} - 88 q^{9} - 108 q^{10} + 20 q^{12} - 16 q^{13} + 64 q^{14} - 30 q^{15} - 168 q^{16} - 4 q^{18} - 8 q^{19} + 64 q^{20} + 32 q^{21} - 24 q^{22} + 24 q^{23} - 72 q^{24} - 248 q^{25} + 32 q^{26} + 48 q^{27} - 88 q^{28} + 48 q^{29} - 58 q^{30} - 120 q^{31} - 48 q^{32} - 8 q^{33} - 120 q^{34} + 52 q^{35} - 116 q^{36} - 96 q^{37} - 80 q^{38} - 92 q^{39} - 260 q^{40} - 88 q^{41} - 108 q^{42} - 216 q^{43} - 112 q^{44} - 24 q^{45} - 328 q^{46} - 208 q^{47} - 188 q^{48} - 392 q^{49} - 104 q^{50} - 340 q^{51} - 72 q^{52} - 120 q^{53} - 116 q^{54} - 188 q^{55} - 32 q^{56} - 176 q^{57} - 120 q^{58} - 136 q^{59} - 210 q^{60} - 96 q^{61} - 16 q^{62} - 172 q^{63} - 184 q^{64} + 32 q^{65} - 128 q^{66} - 136 q^{67} - 112 q^{68} - 408 q^{70} - 32 q^{71} - 188 q^{72} - 16 q^{73} - 24 q^{74} - 84 q^{75} + 112 q^{76} + 252 q^{78} + 48 q^{79} + 236 q^{80} + 96 q^{81} + 184 q^{82} + 104 q^{83} + 428 q^{84} + 260 q^{85} + 912 q^{86} + 232 q^{87} + 712 q^{88} + 344 q^{89} + 280 q^{90} + 480 q^{91} + 800 q^{92} + 64 q^{93} + 960 q^{94} + 216 q^{95} + 928 q^{96} + 136 q^{97} + 904 q^{98} + 176 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2760))\)

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
2760.2.a \(\chi_{2760}(1, \cdot)\) 2760.2.a.a 1 1
2760.2.a.b 1
2760.2.a.c 1
2760.2.a.d 1
2760.2.a.e 1
2760.2.a.f 1
2760.2.a.g 1
2760.2.a.h 1
2760.2.a.i 1
2760.2.a.j 1
2760.2.a.k 1
2760.2.a.l 2
2760.2.a.m 2
2760.2.a.n 2
2760.2.a.o 2
2760.2.a.p 2
2760.2.a.q 2
2760.2.a.r 3
2760.2.a.s 3
2760.2.a.t 3
2760.2.a.u 3
2760.2.a.v 4
2760.2.a.w 5
2760.2.c \(\chi_{2760}(2531, \cdot)\) n/a 352 1
2760.2.e \(\chi_{2760}(2621, \cdot)\) n/a 384 1
2760.2.f \(\chi_{2760}(829, \cdot)\) n/a 264 1
2760.2.h \(\chi_{2760}(2299, \cdot)\) n/a 288 1
2760.2.k \(\chi_{2760}(2209, \cdot)\) 2760.2.k.a 2 1
2760.2.k.b 2
2760.2.k.c 12
2760.2.k.d 14
2760.2.k.e 16
2760.2.k.f 22
2760.2.m \(\chi_{2760}(919, \cdot)\) None 0 1
2760.2.n \(\chi_{2760}(1151, \cdot)\) None 0 1
2760.2.p \(\chi_{2760}(1241, \cdot)\) 2760.2.p.a 48 1
2760.2.p.b 48
2760.2.r \(\chi_{2760}(91, \cdot)\) n/a 192 1
2760.2.t \(\chi_{2760}(1381, \cdot)\) n/a 176 1
2760.2.w \(\chi_{2760}(2069, \cdot)\) n/a 568 1
2760.2.y \(\chi_{2760}(1979, \cdot)\) n/a 528 1
2760.2.z \(\chi_{2760}(689, \cdot)\) n/a 144 1
2760.2.bb \(\chi_{2760}(599, \cdot)\) None 0 1
2760.2.be \(\chi_{2760}(1471, \cdot)\) None 0 1
2760.2.bi \(\chi_{2760}(1103, \cdot)\) None 0 2
2760.2.bj \(\chi_{2760}(737, \cdot)\) n/a 264 2
2760.2.bk \(\chi_{2760}(967, \cdot)\) None 0 2
2760.2.bl \(\chi_{2760}(1057, \cdot)\) n/a 144 2
2760.2.bq \(\chi_{2760}(1243, \cdot)\) n/a 528 2
2760.2.br \(\chi_{2760}(1333, \cdot)\) n/a 576 2
2760.2.bs \(\chi_{2760}(827, \cdot)\) n/a 1136 2
2760.2.bt \(\chi_{2760}(1013, \cdot)\) n/a 1056 2
2760.2.bw \(\chi_{2760}(121, \cdot)\) n/a 480 10
2760.2.by \(\chi_{2760}(511, \cdot)\) None 0 10
2760.2.cb \(\chi_{2760}(119, \cdot)\) None 0 10
2760.2.cd \(\chi_{2760}(89, \cdot)\) n/a 1440 10
2760.2.ce \(\chi_{2760}(59, \cdot)\) n/a 5680 10
2760.2.cg \(\chi_{2760}(149, \cdot)\) n/a 5680 10
2760.2.cj \(\chi_{2760}(301, \cdot)\) n/a 1920 10
2760.2.cl \(\chi_{2760}(451, \cdot)\) n/a 1920 10
2760.2.cn \(\chi_{2760}(281, \cdot)\) n/a 960 10
2760.2.cp \(\chi_{2760}(71, \cdot)\) None 0 10
2760.2.cq \(\chi_{2760}(79, \cdot)\) None 0 10
2760.2.cs \(\chi_{2760}(49, \cdot)\) n/a 720 10
2760.2.cv \(\chi_{2760}(19, \cdot)\) n/a 2880 10
2760.2.cx \(\chi_{2760}(349, \cdot)\) n/a 2880 10
2760.2.cy \(\chi_{2760}(221, \cdot)\) n/a 3840 10
2760.2.da \(\chi_{2760}(131, \cdot)\) n/a 3840 10
2760.2.de \(\chi_{2760}(77, \cdot)\) n/a 11360 20
2760.2.df \(\chi_{2760}(83, \cdot)\) n/a 11360 20
2760.2.dg \(\chi_{2760}(37, \cdot)\) n/a 5760 20
2760.2.dh \(\chi_{2760}(163, \cdot)\) n/a 5760 20
2760.2.dm \(\chi_{2760}(97, \cdot)\) n/a 1440 20
2760.2.dn \(\chi_{2760}(127, \cdot)\) None 0 20
2760.2.do \(\chi_{2760}(233, \cdot)\) n/a 2880 20
2760.2.dp \(\chi_{2760}(143, \cdot)\) None 0 20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1380))\)\(^{\oplus 2}\)