# Properties

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

## 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

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