Properties

Label 483.2
Level 483
Weight 2
Dimension 5843
Nonzero newspaces 16
Newform subspaces 43
Sturm bound 33792
Trace bound 3

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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

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

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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(483)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 1}\)