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Properties

Label 447.2
Level 447
Weight 2
Dimension 5401
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 29600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 447 = 3 \cdot 149 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(29600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(447))\).

Total New Old
Modular forms 7696 5697 1999
Cusp forms 7105 5401 1704
Eisenstein series 591 296 295

Trace form

\( 5401 q - 3 q^{2} - 75 q^{3} - 155 q^{4} - 6 q^{5} - 77 q^{6} - 156 q^{7} - 15 q^{8} - 75 q^{9} + O(q^{10}) \) \( 5401 q - 3 q^{2} - 75 q^{3} - 155 q^{4} - 6 q^{5} - 77 q^{6} - 156 q^{7} - 15 q^{8} - 75 q^{9} - 166 q^{10} - 12 q^{11} - 81 q^{12} - 162 q^{13} - 24 q^{14} - 80 q^{15} - 179 q^{16} - 18 q^{17} - 77 q^{18} - 168 q^{19} - 42 q^{20} - 82 q^{21} - 184 q^{22} - 24 q^{23} - 89 q^{24} - 179 q^{25} - 42 q^{26} - 75 q^{27} - 204 q^{28} - 30 q^{29} - 92 q^{30} - 180 q^{31} - 63 q^{32} - 86 q^{33} - 202 q^{34} - 48 q^{35} - 81 q^{36} - 186 q^{37} - 60 q^{38} - 88 q^{39} - 238 q^{40} - 42 q^{41} - 98 q^{42} - 192 q^{43} - 84 q^{44} - 80 q^{45} - 220 q^{46} - 48 q^{47} - 105 q^{48} - 205 q^{49} - 93 q^{50} - 92 q^{51} - 246 q^{52} - 54 q^{53} - 77 q^{54} - 220 q^{55} - 120 q^{56} - 94 q^{57} - 238 q^{58} - 60 q^{59} - 116 q^{60} - 210 q^{61} - 96 q^{62} - 82 q^{63} - 275 q^{64} - 84 q^{65} - 110 q^{66} - 216 q^{67} - 126 q^{68} - 98 q^{69} - 292 q^{70} - 72 q^{71} - 89 q^{72} - 222 q^{73} - 114 q^{74} - 105 q^{75} - 288 q^{76} - 96 q^{77} - 116 q^{78} - 228 q^{79} - 186 q^{80} - 75 q^{81} - 274 q^{82} - 84 q^{83} - 130 q^{84} - 256 q^{85} - 132 q^{86} - 104 q^{87} - 328 q^{88} - 90 q^{89} - 92 q^{90} - 260 q^{91} - 168 q^{92} - 106 q^{93} - 292 q^{94} - 120 q^{95} - 137 q^{96} - 246 q^{97} - 171 q^{98} - 86 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(447))\)

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
447.2.a \(\chi_{447}(1, \cdot)\) 447.2.a.a 3 1
447.2.a.b 3
447.2.a.c 9
447.2.a.d 10
447.2.c \(\chi_{447}(148, \cdot)\) 447.2.c.a 24 1
447.2.e \(\chi_{447}(44, \cdot)\) 447.2.e.a 96 2
447.2.g \(\chi_{447}(16, \cdot)\) 447.2.g.a 468 36
447.2.g.b 468
447.2.i \(\chi_{447}(4, \cdot)\) 447.2.i.a 864 36
447.2.l \(\chi_{447}(2, \cdot)\) 447.2.l.a 3456 72

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(447))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(447)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(149))\)\(^{\oplus 2}\)