## Defining parameters

 Level: $$N$$ = $$483 = 3 \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$43$$ Sturm bound: $$33792$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(483))$$.

Total New Old
Modular forms 8976 6259 2717
Cusp forms 7921 5843 2078
Eisenstein series 1055 416 639

## Trace form

 $$5843q + 9q^{2} - 37q^{3} - 71q^{4} + 6q^{5} - 47q^{6} - 99q^{7} + 9q^{8} - 49q^{9} + O(q^{10})$$ $$5843q + 9q^{2} - 37q^{3} - 71q^{4} + 6q^{5} - 47q^{6} - 99q^{7} + 9q^{8} - 49q^{9} - 82q^{10} - 43q^{12} - 74q^{13} - 3q^{14} - 114q^{15} - 143q^{16} - 14q^{17} - 123q^{18} - 100q^{19} - 122q^{20} - 81q^{21} - 292q^{22} - 65q^{23} - 211q^{24} - 155q^{25} - 46q^{26} - 115q^{27} - 225q^{28} - 26q^{29} - 126q^{30} - 112q^{31} - 31q^{32} - 66q^{33} - 134q^{34} - 38q^{35} - 129q^{36} - 230q^{37} - 148q^{38} - 118q^{39} - 338q^{40} - 10q^{41} - 144q^{42} - 344q^{43} - 224q^{44} - 60q^{45} - 371q^{46} - 140q^{47} - 215q^{48} - 239q^{49} - 209q^{50} - 102q^{51} - 418q^{52} - 22q^{53} - 35q^{54} - 192q^{55} - 89q^{56} - 160q^{57} - 206q^{58} - 76q^{59} + 162q^{60} - 26q^{61} + 24q^{62} - 29q^{63} - 107q^{64} + 72q^{65} + 102q^{66} - 16q^{67} + 114q^{68} + 89q^{69} - 166q^{70} + 96q^{71} + 229q^{72} + 46q^{73} + 94q^{74} + 83q^{75} - 168q^{76} - 52q^{77} - 168q^{78} - 180q^{79} - 198q^{80} - 201q^{81} - 262q^{82} - 92q^{83} - 130q^{84} - 576q^{85} - 296q^{86} - 266q^{87} - 460q^{88} - 114q^{89} - 388q^{90} - 306q^{91} - 235q^{92} - 272q^{93} - 452q^{94} - 264q^{95} - 405q^{96} - 398q^{97} - 113q^{98} - 406q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(483))$$

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
483.2.a $$\chi_{483}(1, \cdot)$$ 483.2.a.a 1 1
483.2.a.b 1
483.2.a.c 2
483.2.a.d 2
483.2.a.e 2
483.2.a.f 2
483.2.a.g 2
483.2.a.h 3
483.2.a.i 4
483.2.a.j 4
483.2.d $$\chi_{483}(461, \cdot)$$ 483.2.d.a 4 1
483.2.d.b 4
483.2.d.c 8
483.2.d.d 44
483.2.e $$\chi_{483}(344, \cdot)$$ 483.2.e.a 48 1
483.2.h $$\chi_{483}(160, \cdot)$$ 483.2.h.a 8 1
483.2.h.b 12
483.2.h.c 12
483.2.i $$\chi_{483}(277, \cdot)$$ 483.2.i.a 2 2
483.2.i.b 2
483.2.i.c 2
483.2.i.d 2
483.2.i.e 4
483.2.i.f 12
483.2.i.g 16
483.2.i.h 20
483.2.j $$\chi_{483}(229, \cdot)$$ 483.2.j.a 64 2
483.2.m $$\chi_{483}(137, \cdot)$$ 483.2.m.a 120 2
483.2.n $$\chi_{483}(47, \cdot)$$ 483.2.n.a 116 2
483.2.q $$\chi_{483}(64, \cdot)$$ 483.2.q.a 10 10
483.2.q.b 10
483.2.q.c 20
483.2.q.d 60
483.2.q.e 60
483.2.q.f 80
483.2.r $$\chi_{483}(34, \cdot)$$ 483.2.r.a 320 10
483.2.u $$\chi_{483}(113, \cdot)$$ 483.2.u.a 480 10
483.2.v $$\chi_{483}(41, \cdot)$$ 483.2.v.a 600 10
483.2.y $$\chi_{483}(4, \cdot)$$ 483.2.y.a 320 20
483.2.y.b 320
483.2.bb $$\chi_{483}(26, \cdot)$$ 483.2.bb.a 1200 20
483.2.bc $$\chi_{483}(11, \cdot)$$ 483.2.bc.a 1200 20
483.2.bf $$\chi_{483}(10, \cdot)$$ 483.2.bf.a 640 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(483))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(483)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 2}$$