# Properties

 Label 760.2 Level 760 Weight 2 Dimension 8656 Nonzero newspaces 27 Newform subspaces 68 Sturm bound 69120 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$760 = 2^{3} \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$27$$ Newform subspaces: $$68$$ Sturm bound: $$69120$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(760))$$.

Total New Old
Modular forms 18144 9064 9080
Cusp forms 16417 8656 7761
Eisenstein series 1727 408 1319

## Trace form

 $$8656 q - 28 q^{2} - 28 q^{3} - 28 q^{4} + 2 q^{5} - 92 q^{6} - 20 q^{7} - 28 q^{8} - 46 q^{9} + O(q^{10})$$ $$8656 q - 28 q^{2} - 28 q^{3} - 28 q^{4} + 2 q^{5} - 92 q^{6} - 20 q^{7} - 28 q^{8} - 46 q^{9} - 46 q^{10} - 84 q^{11} - 52 q^{12} + 4 q^{13} - 52 q^{14} - 62 q^{15} - 124 q^{16} - 60 q^{17} - 84 q^{18} - 48 q^{19} - 140 q^{20} - 16 q^{21} - 68 q^{22} - 36 q^{23} - 84 q^{24} - 82 q^{25} - 124 q^{26} - 34 q^{27} - 20 q^{28} + 48 q^{29} - 54 q^{30} - 72 q^{31} + 12 q^{32} + 52 q^{33} + 36 q^{34} - 34 q^{35} - 28 q^{36} + 24 q^{37} - 12 q^{38} + 20 q^{39} + 34 q^{40} - 144 q^{41} + 12 q^{42} - 4 q^{43} - 4 q^{44} + 56 q^{45} - 44 q^{46} - 48 q^{47} - 20 q^{48} - 50 q^{49} - 86 q^{50} - 106 q^{51} - 76 q^{52} - 12 q^{53} - 192 q^{54} - 110 q^{55} - 204 q^{56} - 88 q^{57} - 160 q^{58} - 76 q^{59} - 170 q^{60} + 8 q^{61} - 328 q^{62} - 164 q^{63} - 388 q^{64} - 190 q^{65} - 428 q^{66} - 212 q^{67} - 328 q^{68} - 16 q^{69} - 270 q^{70} - 168 q^{71} - 552 q^{72} - 286 q^{73} - 284 q^{74} + 44 q^{75} - 468 q^{76} - 76 q^{77} - 268 q^{78} - 128 q^{79} - 150 q^{80} - 384 q^{81} - 504 q^{82} - 24 q^{83} - 404 q^{84} - 4 q^{85} - 376 q^{86} - 156 q^{87} - 324 q^{88} - 208 q^{89} - 190 q^{90} - 220 q^{91} - 184 q^{92} - 36 q^{93} - 172 q^{94} - 6 q^{95} - 312 q^{96} + 28 q^{97} - 60 q^{98} + 98 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$

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
760.2.a $$\chi_{760}(1, \cdot)$$ 760.2.a.a 1 1
760.2.a.b 1
760.2.a.c 1
760.2.a.d 1
760.2.a.e 1
760.2.a.f 2
760.2.a.g 2
760.2.a.h 3
760.2.a.i 3
760.2.a.j 3
760.2.d $$\chi_{760}(609, \cdot)$$ 760.2.d.a 2 1
760.2.d.b 4
760.2.d.c 4
760.2.d.d 4
760.2.d.e 12
760.2.e $$\chi_{760}(531, \cdot)$$ 760.2.e.a 80 1
760.2.f $$\chi_{760}(381, \cdot)$$ 760.2.f.a 28 1
760.2.f.b 44
760.2.g $$\chi_{760}(759, \cdot)$$ None 0 1
760.2.j $$\chi_{760}(151, \cdot)$$ None 0 1
760.2.k $$\chi_{760}(229, \cdot)$$ 760.2.k.a 108 1
760.2.p $$\chi_{760}(379, \cdot)$$ 760.2.p.a 4 1
760.2.p.b 4
760.2.p.c 4
760.2.p.d 8
760.2.p.e 8
760.2.p.f 8
760.2.p.g 8
760.2.p.h 16
760.2.p.i 56
760.2.q $$\chi_{760}(121, \cdot)$$ 760.2.q.a 2 2
760.2.q.b 2
760.2.q.c 2
760.2.q.d 8
760.2.q.e 8
760.2.q.f 8
760.2.q.g 10
760.2.t $$\chi_{760}(37, \cdot)$$ 760.2.t.a 232 2
760.2.u $$\chi_{760}(343, \cdot)$$ None 0 2
760.2.v $$\chi_{760}(113, \cdot)$$ 760.2.v.a 12 2
760.2.v.b 48
760.2.w $$\chi_{760}(267, \cdot)$$ 760.2.w.a 2 2
760.2.w.b 2
760.2.w.c 104
760.2.w.d 108
760.2.z $$\chi_{760}(349, \cdot)$$ 760.2.z.a 232 2
760.2.ba $$\chi_{760}(31, \cdot)$$ None 0 2
760.2.bf $$\chi_{760}(179, \cdot)$$ 760.2.bf.a 8 2
760.2.bf.b 224
760.2.bi $$\chi_{760}(331, \cdot)$$ 760.2.bi.a 160 2
760.2.bj $$\chi_{760}(49, \cdot)$$ 760.2.bj.a 4 2
760.2.bj.b 56
760.2.bk $$\chi_{760}(559, \cdot)$$ None 0 2
760.2.bl $$\chi_{760}(501, \cdot)$$ 760.2.bl.a 4 2
760.2.bl.b 4
760.2.bl.c 152
760.2.bo $$\chi_{760}(81, \cdot)$$ 760.2.bo.a 24 6
760.2.bo.b 30
760.2.bo.c 30
760.2.bo.d 36
760.2.bp $$\chi_{760}(293, \cdot)$$ 760.2.bp.a 464 4
760.2.bq $$\chi_{760}(7, \cdot)$$ None 0 4
760.2.bv $$\chi_{760}(217, \cdot)$$ 760.2.bv.a 120 4
760.2.bw $$\chi_{760}(83, \cdot)$$ 760.2.bw.a 8 4
760.2.bw.b 456
760.2.bx $$\chi_{760}(59, \cdot)$$ 760.2.bx.a 24 6
760.2.bx.b 672
760.2.cc $$\chi_{760}(61, \cdot)$$ 760.2.cc.a 480 6
760.2.cd $$\chi_{760}(79, \cdot)$$ None 0 6
760.2.cg $$\chi_{760}(9, \cdot)$$ 760.2.cg.a 180 6
760.2.ch $$\chi_{760}(51, \cdot)$$ 760.2.ch.a 480 6
760.2.ci $$\chi_{760}(71, \cdot)$$ None 0 6
760.2.cj $$\chi_{760}(149, \cdot)$$ 760.2.cj.a 696 6
760.2.co $$\chi_{760}(33, \cdot)$$ 760.2.co.a 360 12
760.2.cp $$\chi_{760}(43, \cdot)$$ 760.2.cp.a 1392 12
760.2.cs $$\chi_{760}(13, \cdot)$$ 760.2.cs.a 1392 12
760.2.ct $$\chi_{760}(23, \cdot)$$ None 0 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(760))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(760)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$$$^{\oplus 1}$$