Properties

Label 2760.3
Level 2760
Weight 3
Dimension 155720
Nonzero newspaces 36
Sturm bound 1216512
Trace bound 20

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Defining parameters

Level: \( N \) = \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(1216512\)
Trace bound: \(20\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2760))\).

Total New Old
Modular forms 409728 156728 253000
Cusp forms 401280 155720 245560
Eisenstein series 8448 1008 7440

Trace form

\( 155720 q + 8 q^{2} - 28 q^{3} - 120 q^{4} + 16 q^{5} - 172 q^{6} - 104 q^{7} - 16 q^{8} - 88 q^{9} + O(q^{10}) \) \( 155720 q + 8 q^{2} - 28 q^{3} - 120 q^{4} + 16 q^{5} - 172 q^{6} - 104 q^{7} - 16 q^{8} - 88 q^{9} - 140 q^{10} - 160 q^{11} - 44 q^{12} - 72 q^{13} - 96 q^{14} - 178 q^{15} - 296 q^{16} - 88 q^{17} + 156 q^{18} + 56 q^{19} + 224 q^{20} - 64 q^{21} + 360 q^{22} + 96 q^{23} - 8 q^{24} - 304 q^{25} + 64 q^{26} - 76 q^{27} - 88 q^{28} + 86 q^{30} - 680 q^{31} + 208 q^{32} - 40 q^{33} + 296 q^{34} + 248 q^{35} + 364 q^{36} + 1288 q^{37} + 272 q^{38} + 1348 q^{39} + 220 q^{40} + 928 q^{41} + 708 q^{42} + 1768 q^{43} - 304 q^{44} + 328 q^{45} - 392 q^{46} + 480 q^{47} - 284 q^{48} - 1120 q^{49} - 1016 q^{50} - 868 q^{51} - 1544 q^{52} - 680 q^{53} - 324 q^{54} - 1156 q^{55} - 672 q^{56} - 1192 q^{57} - 56 q^{58} - 1744 q^{59} + 46 q^{60} - 784 q^{61} + 816 q^{62} - 812 q^{63} + 1608 q^{64} - 296 q^{65} + 400 q^{66} + 200 q^{67} + 1680 q^{68} - 368 q^{69} + 1128 q^{70} + 960 q^{71} - 732 q^{72} + 136 q^{73} - 1096 q^{74} - 1122 q^{75} - 7248 q^{76} - 480 q^{77} - 6564 q^{78} - 2744 q^{79} - 4708 q^{80} - 2304 q^{81} - 7848 q^{82} - 3328 q^{83} - 5844 q^{84} - 1584 q^{85} - 7440 q^{86} - 1276 q^{87} - 6072 q^{88} + 272 q^{89} - 2140 q^{90} - 2336 q^{91} - 512 q^{92} + 448 q^{93} - 1328 q^{94} - 416 q^{95} + 2288 q^{96} + 3032 q^{97} + 4472 q^{98} + 3796 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2760))\)

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
2760.3.b \(\chi_{2760}(2759, \cdot)\) None 0 1
2760.3.d \(\chi_{2760}(1289, \cdot)\) n/a 264 1
2760.3.g \(\chi_{2760}(2161, \cdot)\) 2760.3.g.a 96 1
2760.3.i \(\chi_{2760}(2071, \cdot)\) None 0 1
2760.3.j \(\chi_{2760}(781, \cdot)\) n/a 384 1
2760.3.l \(\chi_{2760}(691, \cdot)\) n/a 352 1
2760.3.o \(\chi_{2760}(1379, \cdot)\) n/a 1144 1
2760.3.q \(\chi_{2760}(2669, \cdot)\) n/a 1056 1
2760.3.s \(\chi_{2760}(1519, \cdot)\) None 0 1
2760.3.u \(\chi_{2760}(1609, \cdot)\) n/a 144 1
2760.3.v \(\chi_{2760}(1841, \cdot)\) n/a 176 1
2760.3.x \(\chi_{2760}(551, \cdot)\) None 0 1
2760.3.ba \(\chi_{2760}(461, \cdot)\) n/a 704 1
2760.3.bc \(\chi_{2760}(1931, \cdot)\) n/a 768 1
2760.3.bd \(\chi_{2760}(139, \cdot)\) n/a 528 1
2760.3.bf \(\chi_{2760}(229, \cdot)\) n/a 576 1
2760.3.bg \(\chi_{2760}(323, \cdot)\) n/a 2112 2
2760.3.bh \(\chi_{2760}(413, \cdot)\) n/a 2288 2
2760.3.bm \(\chi_{2760}(643, \cdot)\) n/a 1152 2
2760.3.bn \(\chi_{2760}(277, \cdot)\) n/a 1056 2
2760.3.bo \(\chi_{2760}(367, \cdot)\) None 0 2
2760.3.bp \(\chi_{2760}(553, \cdot)\) n/a 264 2
2760.3.bu \(\chi_{2760}(47, \cdot)\) None 0 2
2760.3.bv \(\chi_{2760}(137, \cdot)\) n/a 576 2
2760.3.bx \(\chi_{2760}(109, \cdot)\) n/a 5760 10
2760.3.bz \(\chi_{2760}(259, \cdot)\) n/a 5760 10
2760.3.ca \(\chi_{2760}(11, \cdot)\) n/a 7680 10
2760.3.cc \(\chi_{2760}(101, \cdot)\) n/a 7680 10
2760.3.cf \(\chi_{2760}(191, \cdot)\) None 0 10
2760.3.ch \(\chi_{2760}(41, \cdot)\) n/a 1920 10
2760.3.ci \(\chi_{2760}(649, \cdot)\) n/a 1440 10
2760.3.ck \(\chi_{2760}(439, \cdot)\) None 0 10
2760.3.cm \(\chi_{2760}(29, \cdot)\) n/a 11440 10
2760.3.co \(\chi_{2760}(419, \cdot)\) n/a 11440 10
2760.3.cr \(\chi_{2760}(211, \cdot)\) n/a 3840 10
2760.3.ct \(\chi_{2760}(61, \cdot)\) n/a 3840 10
2760.3.cu \(\chi_{2760}(31, \cdot)\) None 0 10
2760.3.cw \(\chi_{2760}(241, \cdot)\) n/a 960 10
2760.3.cz \(\chi_{2760}(209, \cdot)\) n/a 2880 10
2760.3.db \(\chi_{2760}(359, \cdot)\) None 0 10
2760.3.dc \(\chi_{2760}(17, \cdot)\) n/a 5760 20
2760.3.dd \(\chi_{2760}(167, \cdot)\) None 0 20
2760.3.di \(\chi_{2760}(73, \cdot)\) n/a 2880 20
2760.3.dj \(\chi_{2760}(7, \cdot)\) None 0 20
2760.3.dk \(\chi_{2760}(13, \cdot)\) n/a 11520 20
2760.3.dl \(\chi_{2760}(43, \cdot)\) n/a 11520 20
2760.3.dq \(\chi_{2760}(53, \cdot)\) n/a 22880 20
2760.3.dr \(\chi_{2760}(347, \cdot)\) n/a 22880 20

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2760))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2760)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1380))\)\(^{\oplus 2}\)