## Defining parameters

 Level: $$N$$ = $$495 = 3^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$65$$ Sturm bound: $$34560$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(495))$$.

Total New Old
Modular forms 9280 6410 2870
Cusp forms 8001 5922 2079
Eisenstein series 1279 488 791

## Trace form

 $$5922q - 16q^{2} - 24q^{3} - 8q^{4} - 27q^{5} - 88q^{6} + 4q^{7} - 4q^{8} - 32q^{9} + O(q^{10})$$ $$5922q - 16q^{2} - 24q^{3} - 8q^{4} - 27q^{5} - 88q^{6} + 4q^{7} - 4q^{8} - 32q^{9} - 90q^{10} - 76q^{11} - 96q^{12} - 16q^{13} - 24q^{14} - 68q^{15} - 16q^{16} - 4q^{17} - 72q^{18} - 20q^{19} - 100q^{20} - 120q^{21} + 22q^{22} - 94q^{23} - 172q^{24} - 61q^{25} - 188q^{26} - 132q^{27} - 236q^{28} - 144q^{29} - 184q^{30} - 114q^{31} - 276q^{32} - 148q^{33} - 168q^{34} - 84q^{35} - 196q^{36} - 114q^{37} - 128q^{38} - 36q^{39} - 114q^{40} - 20q^{41} - 88q^{42} + 4q^{43} - 22q^{44} - 74q^{45} - 140q^{46} + 60q^{47} - 40q^{48} - 26q^{49} - 8q^{50} - 108q^{51} - 184q^{52} - 144q^{53} - 192q^{54} - 247q^{55} - 568q^{56} - 232q^{57} - 392q^{58} - 358q^{59} - 240q^{60} - 292q^{61} - 668q^{62} - 320q^{63} - 648q^{64} - 334q^{65} - 468q^{66} - 358q^{67} - 600q^{68} - 320q^{69} - 310q^{70} - 398q^{71} - 388q^{72} - 116q^{73} - 356q^{74} - 64q^{75} - 212q^{76} - 168q^{77} - 200q^{78} + 4q^{79} + 130q^{80} - 40q^{81} - 100q^{82} + 304q^{83} + 284q^{84} + 32q^{85} + 400q^{86} + 248q^{87} + 130q^{88} + 302q^{89} + 348q^{90} - 224q^{91} + 472q^{92} + 280q^{93} - 12q^{94} + 150q^{95} + 572q^{96} - 34q^{97} + 436q^{98} + 300q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(495))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
495.2.a $$\chi_{495}(1, \cdot)$$ 495.2.a.a 1 1
495.2.a.b 2
495.2.a.c 2
495.2.a.d 2
495.2.a.e 3
495.2.a.f 4
495.2.a.g 4
495.2.c $$\chi_{495}(199, \cdot)$$ 495.2.c.a 4 1
495.2.c.b 4
495.2.c.c 4
495.2.c.d 6
495.2.c.e 6
495.2.d $$\chi_{495}(494, \cdot)$$ 495.2.d.a 4 1
495.2.d.b 4
495.2.d.c 16
495.2.f $$\chi_{495}(296, \cdot)$$ 495.2.f.a 16 1
495.2.i $$\chi_{495}(166, \cdot)$$ 495.2.i.a 2 2
495.2.i.b 2
495.2.i.c 16
495.2.i.d 18
495.2.i.e 20
495.2.i.f 22
495.2.k $$\chi_{495}(208, \cdot)$$ 495.2.k.a 4 2
495.2.k.b 4
495.2.k.c 24
495.2.k.d 24
495.2.l $$\chi_{495}(188, \cdot)$$ 495.2.l.a 20 2
495.2.l.b 20
495.2.n $$\chi_{495}(91, \cdot)$$ 495.2.n.a 8 4
495.2.n.b 8
495.2.n.c 8
495.2.n.d 8
495.2.n.e 8
495.2.n.f 8
495.2.n.g 16
495.2.n.h 16
495.2.p $$\chi_{495}(131, \cdot)$$ 495.2.p.a 96 2
495.2.r $$\chi_{495}(164, \cdot)$$ 495.2.r.a 4 2
495.2.r.b 4
495.2.r.c 128
495.2.u $$\chi_{495}(34, \cdot)$$ 495.2.u.a 52 2
495.2.u.b 68
495.2.x $$\chi_{495}(116, \cdot)$$ 495.2.x.a 64 4
495.2.z $$\chi_{495}(134, \cdot)$$ 495.2.z.a 96 4
495.2.ba $$\chi_{495}(64, \cdot)$$ 495.2.ba.a 16 4
495.2.ba.b 48
495.2.ba.c 48
495.2.bc $$\chi_{495}(23, \cdot)$$ 495.2.bc.a 4 4
495.2.bc.b 4
495.2.bc.c 116
495.2.bc.d 116
495.2.bf $$\chi_{495}(43, \cdot)$$ 495.2.bf.a 8 4
495.2.bf.b 8
495.2.bf.c 256
495.2.bg $$\chi_{495}(16, \cdot)$$ 495.2.bg.a 192 8
495.2.bg.b 192
495.2.bi $$\chi_{495}(53, \cdot)$$ 495.2.bi.a 192 8
495.2.bj $$\chi_{495}(28, \cdot)$$ 495.2.bj.a 32 8
495.2.bj.b 96
495.2.bj.c 96
495.2.bl $$\chi_{495}(4, \cdot)$$ 495.2.bl.a 544 8
495.2.bo $$\chi_{495}(29, \cdot)$$ 495.2.bo.a 544 8
495.2.bq $$\chi_{495}(41, \cdot)$$ 495.2.bq.a 384 8
495.2.bs $$\chi_{495}(7, \cdot)$$ 495.2.bs.a 1088 16
495.2.bv $$\chi_{495}(38, \cdot)$$ 495.2.bv.a 1088 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(495))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(495)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 2}$$