# Properties

 Label 740.4 Level 740 Weight 4 Dimension 26084 Nonzero newspaces 30 Sturm bound 131328 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$740 = 2^{2} \cdot 5 \cdot 37$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$30$$ Sturm bound: $$131328$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(740))$$.

Total New Old
Modular forms 49968 26500 23468
Cusp forms 48528 26084 22444
Eisenstein series 1440 416 1024

## Trace form

 $$26084 q - 32 q^{2} - 8 q^{3} - 36 q^{4} - 138 q^{5} - 124 q^{6} + 32 q^{7} + 52 q^{8} + 146 q^{9} + O(q^{10})$$ $$26084 q - 32 q^{2} - 8 q^{3} - 36 q^{4} - 138 q^{5} - 124 q^{6} + 32 q^{7} + 52 q^{8} + 146 q^{9} + 94 q^{10} + 40 q^{11} + 124 q^{12} - 328 q^{13} - 36 q^{14} - 344 q^{15} - 476 q^{16} + 160 q^{17} - 648 q^{18} + 248 q^{19} - 686 q^{20} - 104 q^{21} - 756 q^{22} - 96 q^{23} - 36 q^{24} - 262 q^{25} + 812 q^{26} + 2896 q^{27} + 1724 q^{28} + 996 q^{29} + 2426 q^{30} - 104 q^{31} + 1228 q^{32} - 1480 q^{33} - 36 q^{34} - 1372 q^{35} - 1928 q^{36} - 3676 q^{37} - 3272 q^{38} - 5032 q^{39} - 3726 q^{40} - 3956 q^{41} - 2356 q^{42} + 632 q^{43} - 36 q^{44} + 2146 q^{45} + 2756 q^{46} + 2328 q^{47} + 5404 q^{48} + 4794 q^{49} + 4374 q^{50} + 2288 q^{51} + 3012 q^{52} + 2320 q^{53} - 36 q^{54} + 40 q^{55} - 4204 q^{56} + 1496 q^{57} - 11472 q^{58} - 9248 q^{59} - 20348 q^{60} - 4634 q^{61} - 15536 q^{62} - 8344 q^{63} - 4320 q^{64} + 4493 q^{65} + 11820 q^{66} + 4304 q^{67} + 14108 q^{68} + 16936 q^{69} + 18104 q^{70} + 7680 q^{71} + 40092 q^{72} + 5472 q^{73} + 20988 q^{74} + 8324 q^{75} + 17588 q^{76} + 552 q^{77} + 19236 q^{78} + 5456 q^{79} + 1892 q^{80} - 5154 q^{81} - 892 q^{82} - 3120 q^{83} - 18684 q^{84} - 12063 q^{85} - 15920 q^{86} - 22056 q^{87} - 19896 q^{88} - 6970 q^{89} - 20820 q^{90} - 8960 q^{91} - 6040 q^{92} + 26248 q^{93} - 36 q^{94} + 11272 q^{95} - 2284 q^{96} + 23816 q^{97} - 688 q^{98} + 6560 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(740))$$

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
740.4.a $$\chi_{740}(1, \cdot)$$ 740.4.a.a 1 1
740.4.a.b 5
740.4.a.c 8
740.4.a.d 11
740.4.a.e 11
740.4.d $$\chi_{740}(149, \cdot)$$ 740.4.d.a 54 1
740.4.e $$\chi_{740}(369, \cdot)$$ 740.4.e.a 56 1
740.4.h $$\chi_{740}(221, \cdot)$$ 740.4.h.a 38 1
740.4.i $$\chi_{740}(121, \cdot)$$ 740.4.i.a 38 2
740.4.i.b 38
740.4.k $$\chi_{740}(179, \cdot)$$ n/a 676 2
740.4.l $$\chi_{740}(413, \cdot)$$ n/a 114 2
740.4.m $$\chi_{740}(147, \cdot)$$ n/a 676 2
740.4.n $$\chi_{740}(223, \cdot)$$ n/a 648 2
740.4.o $$\chi_{740}(117, \cdot)$$ n/a 114 2
740.4.u $$\chi_{740}(31, \cdot)$$ n/a 456 2
740.4.x $$\chi_{740}(101, \cdot)$$ 740.4.x.a 76 2
740.4.ba $$\chi_{740}(249, \cdot)$$ n/a 112 2
740.4.bb $$\chi_{740}(269, \cdot)$$ n/a 116 2
740.4.bc $$\chi_{740}(81, \cdot)$$ n/a 228 6
740.4.be $$\chi_{740}(51, \cdot)$$ n/a 912 4
740.4.bf $$\chi_{740}(97, \cdot)$$ n/a 228 4
740.4.bg $$\chi_{740}(47, \cdot)$$ n/a 1352 4
740.4.bh $$\chi_{740}(27, \cdot)$$ n/a 1352 4
740.4.bi $$\chi_{740}(177, \cdot)$$ n/a 228 4
740.4.bo $$\chi_{740}(119, \cdot)$$ n/a 1352 4
740.4.bp $$\chi_{740}(169, \cdot)$$ n/a 336 6
740.4.bq $$\chi_{740}(21, \cdot)$$ n/a 228 6
740.4.br $$\chi_{740}(9, \cdot)$$ n/a 348 6
740.4.bx $$\chi_{740}(91, \cdot)$$ n/a 2736 12
740.4.ca $$\chi_{740}(19, \cdot)$$ n/a 4056 12
740.4.cc $$\chi_{740}(17, \cdot)$$ n/a 684 12
740.4.ce $$\chi_{740}(3, \cdot)$$ n/a 4056 12
740.4.cf $$\chi_{740}(7, \cdot)$$ n/a 4056 12
740.4.ch $$\chi_{740}(13, \cdot)$$ n/a 684 12

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(740))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(740)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(148))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(185))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(370))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(740))$$$$^{\oplus 1}$$