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Properties

Label 453.2
Level 453
Weight 2
Dimension 5549
Nonzero newspaces 12
Newform subspaces 28
Sturm bound 30400
Trace bound 1

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Defining parameters

Level: \( N \) = \( 453 = 3 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 28 \)
Sturm bound: \(30400\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(453))\).

Total New Old
Modular forms 7900 5849 2051
Cusp forms 7301 5549 1752
Eisenstein series 599 300 299

Trace form

\( 5549 q - 3 q^{2} - 76 q^{3} - 157 q^{4} - 6 q^{5} - 78 q^{6} - 158 q^{7} - 15 q^{8} - 76 q^{9} + O(q^{10}) \) \( 5549 q - 3 q^{2} - 76 q^{3} - 157 q^{4} - 6 q^{5} - 78 q^{6} - 158 q^{7} - 15 q^{8} - 76 q^{9} - 168 q^{10} - 12 q^{11} - 82 q^{12} - 164 q^{13} - 24 q^{14} - 81 q^{15} - 181 q^{16} - 18 q^{17} - 78 q^{18} - 170 q^{19} - 42 q^{20} - 83 q^{21} - 186 q^{22} - 24 q^{23} - 90 q^{24} - 181 q^{25} - 42 q^{26} - 76 q^{27} - 206 q^{28} - 30 q^{29} - 93 q^{30} - 182 q^{31} - 63 q^{32} - 87 q^{33} - 204 q^{34} - 48 q^{35} - 82 q^{36} - 188 q^{37} - 60 q^{38} - 89 q^{39} - 240 q^{40} - 42 q^{41} - 99 q^{42} - 194 q^{43} - 84 q^{44} - 81 q^{45} - 222 q^{46} - 48 q^{47} - 106 q^{48} - 207 q^{49} - 93 q^{50} - 93 q^{51} - 248 q^{52} - 54 q^{53} - 78 q^{54} - 222 q^{55} - 120 q^{56} - 95 q^{57} - 240 q^{58} - 60 q^{59} - 117 q^{60} - 212 q^{61} - 96 q^{62} - 83 q^{63} - 277 q^{64} - 84 q^{65} - 111 q^{66} - 218 q^{67} - 126 q^{68} - 99 q^{69} - 294 q^{70} - 72 q^{71} - 90 q^{72} - 224 q^{73} - 114 q^{74} - 106 q^{75} - 290 q^{76} - 96 q^{77} - 117 q^{78} - 230 q^{79} - 186 q^{80} - 76 q^{81} - 276 q^{82} - 84 q^{83} - 131 q^{84} - 258 q^{85} - 132 q^{86} - 105 q^{87} - 330 q^{88} - 90 q^{89} - 93 q^{90} - 262 q^{91} - 168 q^{92} - 107 q^{93} - 294 q^{94} - 120 q^{95} - 138 q^{96} - 248 q^{97} - 171 q^{98} - 87 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(453))\)

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
453.2.a \(\chi_{453}(1, \cdot)\) 453.2.a.a 2 1
453.2.a.b 2
453.2.a.c 2
453.2.a.d 2
453.2.a.e 3
453.2.a.f 5
453.2.a.g 9
453.2.b \(\chi_{453}(452, \cdot)\) 453.2.b.a 48 1
453.2.e \(\chi_{453}(118, \cdot)\) 453.2.e.a 4 2
453.2.e.b 22
453.2.e.c 24
453.2.f \(\chi_{453}(19, \cdot)\) 453.2.f.a 48 4
453.2.f.b 56
453.2.i \(\chi_{453}(119, \cdot)\) 453.2.i.a 2 2
453.2.i.b 12
453.2.i.c 84
453.2.k \(\chi_{453}(92, \cdot)\) 453.2.k.a 192 4
453.2.m \(\chi_{453}(4, \cdot)\) 453.2.m.a 96 8
453.2.m.b 104
453.2.n \(\chi_{453}(91, \cdot)\) 453.2.n.a 240 20
453.2.n.b 280
453.2.p \(\chi_{453}(23, \cdot)\) 453.2.p.a 8 8
453.2.p.b 384
453.2.s \(\chi_{453}(26, \cdot)\) 453.2.s.a 960 20
453.2.u \(\chi_{453}(10, \cdot)\) 453.2.u.a 480 40
453.2.u.b 520
453.2.w \(\chi_{453}(14, \cdot)\) 453.2.w.a 40 40
453.2.w.b 1920

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(453))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(453)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(453))\)\(^{\oplus 1}\)