# Properties

 Label 740.2 Level 740 Weight 2 Dimension 8556 Nonzero newspaces 30 Newform subspaces 58 Sturm bound 65664 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$740 = 2^{2} \cdot 5 \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Newform subspaces: $$58$$ Sturm bound: $$65664$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(740))$$.

Total New Old
Modular forms 17136 8972 8164
Cusp forms 15697 8556 7141
Eisenstein series 1439 416 1023

## Trace form

 $$8556 q - 32 q^{2} + 4 q^{3} - 36 q^{4} - 98 q^{5} - 108 q^{6} - 4 q^{7} - 44 q^{8} - 74 q^{9} + O(q^{10})$$ $$8556 q - 32 q^{2} + 4 q^{3} - 36 q^{4} - 98 q^{5} - 108 q^{6} - 4 q^{7} - 44 q^{8} - 74 q^{9} - 66 q^{10} - 36 q^{12} - 72 q^{13} - 36 q^{14} - 4 q^{15} - 92 q^{16} - 72 q^{17} - 24 q^{18} + 8 q^{19} - 46 q^{20} - 208 q^{21} - 36 q^{22} - 12 q^{23} - 36 q^{24} - 122 q^{25} - 116 q^{26} + 40 q^{27} - 36 q^{28} - 48 q^{29} - 54 q^{30} + 116 q^{31} - 52 q^{32} - 36 q^{34} + 58 q^{35} - 168 q^{36} + 24 q^{37} - 72 q^{38} + 92 q^{39} - 46 q^{40} - 88 q^{41} - 36 q^{42} + 92 q^{43} - 36 q^{44} - 64 q^{45} - 108 q^{46} + 48 q^{47} - 36 q^{48} - 18 q^{49} - 26 q^{50} - 24 q^{51} - 28 q^{52} - 96 q^{53} - 36 q^{54} - 108 q^{56} - 88 q^{57} - 88 q^{58} - 96 q^{59} - 180 q^{60} - 358 q^{61} - 216 q^{62} - 220 q^{63} - 288 q^{64} - 189 q^{65} - 612 q^{66} - 76 q^{67} - 228 q^{68} - 336 q^{69} - 252 q^{70} - 120 q^{71} - 516 q^{72} - 248 q^{73} - 324 q^{74} - 176 q^{75} - 396 q^{76} - 216 q^{77} - 540 q^{78} - 160 q^{79} - 284 q^{80} - 446 q^{81} - 284 q^{82} - 84 q^{83} - 540 q^{84} - 165 q^{85} - 360 q^{86} - 192 q^{87} - 216 q^{88} - 150 q^{89} - 192 q^{90} - 68 q^{91} - 72 q^{92} + 20 q^{93} - 36 q^{94} + 64 q^{95} - 108 q^{96} + 16 q^{97} - 64 q^{98} + 180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(740))$$

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
740.2.a $$\chi_{740}(1, \cdot)$$ 740.2.a.a 1 1
740.2.a.b 1
740.2.a.c 1
740.2.a.d 2
740.2.a.e 3
740.2.a.f 4
740.2.d $$\chi_{740}(149, \cdot)$$ 740.2.d.a 18 1
740.2.e $$\chi_{740}(369, \cdot)$$ 740.2.e.a 20 1
740.2.h $$\chi_{740}(221, \cdot)$$ 740.2.h.a 2 1
740.2.h.b 12
740.2.i $$\chi_{740}(121, \cdot)$$ 740.2.i.a 14 2
740.2.i.b 14
740.2.k $$\chi_{740}(179, \cdot)$$ 740.2.k.a 2 2
740.2.k.b 2
740.2.k.c 216
740.2.l $$\chi_{740}(413, \cdot)$$ 740.2.l.a 6 2
740.2.l.b 32
740.2.m $$\chi_{740}(147, \cdot)$$ 740.2.m.a 2 2
740.2.m.b 2
740.2.m.c 216
740.2.n $$\chi_{740}(223, \cdot)$$ 740.2.n.a 216 2
740.2.o $$\chi_{740}(117, \cdot)$$ 740.2.o.a 6 2
740.2.o.b 32
740.2.u $$\chi_{740}(31, \cdot)$$ 740.2.u.a 152 2
740.2.x $$\chi_{740}(101, \cdot)$$ 740.2.x.a 28 2
740.2.ba $$\chi_{740}(249, \cdot)$$ 740.2.ba.a 40 2
740.2.bb $$\chi_{740}(269, \cdot)$$ 740.2.bb.a 36 2
740.2.bc $$\chi_{740}(81, \cdot)$$ 740.2.bc.a 6 6
740.2.bc.b 12
740.2.bc.c 18
740.2.bc.d 36
740.2.be $$\chi_{740}(51, \cdot)$$ 740.2.be.a 304 4
740.2.bf $$\chi_{740}(97, \cdot)$$ 740.2.bf.a 76 4
740.2.bg $$\chi_{740}(47, \cdot)$$ 740.2.bg.a 4 4
740.2.bg.b 4
740.2.bg.c 432
740.2.bh $$\chi_{740}(27, \cdot)$$ 740.2.bh.a 4 4
740.2.bh.b 4
740.2.bh.c 432
740.2.bi $$\chi_{740}(177, \cdot)$$ 740.2.bi.a 76 4
740.2.bo $$\chi_{740}(119, \cdot)$$ 740.2.bo.a 4 4
740.2.bo.b 4
740.2.bo.c 432
740.2.bp $$\chi_{740}(169, \cdot)$$ 740.2.bp.a 120 6
740.2.bq $$\chi_{740}(21, \cdot)$$ 740.2.bq.a 72 6
740.2.br $$\chi_{740}(9, \cdot)$$ 740.2.br.a 108 6
740.2.bx $$\chi_{740}(91, \cdot)$$ 740.2.bx.a 912 12
740.2.ca $$\chi_{740}(19, \cdot)$$ 740.2.ca.a 12 12
740.2.ca.b 12
740.2.ca.c 1296
740.2.cc $$\chi_{740}(17, \cdot)$$ 740.2.cc.a 228 12
740.2.ce $$\chi_{740}(3, \cdot)$$ 740.2.ce.a 12 12
740.2.ce.b 12
740.2.ce.c 1296
740.2.cf $$\chi_{740}(7, \cdot)$$ 740.2.cf.a 12 12
740.2.cf.b 12
740.2.cf.c 1296
740.2.ch $$\chi_{740}(13, \cdot)$$ 740.2.ch.a 228 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(740))$$ into lower level spaces

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