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Properties

Label 472.2
Level 472
Weight 2
Dimension 3799
Nonzero newspaces 6
Newform subspaces 15
Sturm bound 27840
Trace bound 2

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Defining parameters

Level: \( N \) = \( 472 = 2^{3} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 15 \)
Sturm bound: \(27840\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(472))\).

Total New Old
Modular forms 7308 4027 3281
Cusp forms 6613 3799 2814
Eisenstein series 695 228 467

Trace form

\( 3799 q - 58 q^{2} - 58 q^{3} - 58 q^{4} - 58 q^{6} - 58 q^{7} - 58 q^{8} - 116 q^{9} + O(q^{10}) \) \( 3799 q - 58 q^{2} - 58 q^{3} - 58 q^{4} - 58 q^{6} - 58 q^{7} - 58 q^{8} - 116 q^{9} - 58 q^{10} - 58 q^{11} - 58 q^{12} - 58 q^{14} - 58 q^{15} - 58 q^{16} - 116 q^{17} - 58 q^{18} - 58 q^{19} - 58 q^{20} - 58 q^{22} - 58 q^{23} - 58 q^{24} - 116 q^{25} - 58 q^{26} - 58 q^{27} - 58 q^{28} - 58 q^{30} - 58 q^{31} - 58 q^{32} - 116 q^{33} - 58 q^{34} - 58 q^{35} - 58 q^{36} - 58 q^{38} - 58 q^{39} - 58 q^{40} - 116 q^{41} - 58 q^{42} - 58 q^{43} - 58 q^{44} - 58 q^{46} - 58 q^{47} - 58 q^{48} - 116 q^{49} - 58 q^{50} - 58 q^{51} - 58 q^{52} - 58 q^{54} - 58 q^{55} - 58 q^{56} - 116 q^{57} - 58 q^{58} - 58 q^{59} - 116 q^{60} - 58 q^{62} - 58 q^{63} - 58 q^{64} - 116 q^{65} - 58 q^{66} - 58 q^{67} - 58 q^{68} - 58 q^{70} - 58 q^{71} - 58 q^{72} - 116 q^{73} - 58 q^{74} - 58 q^{75} - 58 q^{76} - 58 q^{78} - 58 q^{79} - 58 q^{80} - 116 q^{81} - 58 q^{82} - 58 q^{83} - 58 q^{84} - 58 q^{86} - 58 q^{87} - 58 q^{88} - 116 q^{89} - 58 q^{90} - 58 q^{91} - 58 q^{92} - 58 q^{94} - 58 q^{95} - 58 q^{96} - 116 q^{97} - 58 q^{98} - 145 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(472))\)

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
472.2.a \(\chi_{472}(1, \cdot)\) 472.2.a.a 1 1
472.2.a.b 1
472.2.a.c 1
472.2.a.d 1
472.2.a.e 1
472.2.a.f 4
472.2.a.g 6
472.2.b \(\chi_{472}(237, \cdot)\) 472.2.b.a 58 1
472.2.e \(\chi_{472}(471, \cdot)\) None 0 1
472.2.f \(\chi_{472}(235, \cdot)\) 472.2.f.a 2 1
472.2.f.b 56
472.2.i \(\chi_{472}(9, \cdot)\) 472.2.i.a 196 28
472.2.i.b 224
472.2.l \(\chi_{472}(11, \cdot)\) 472.2.l.a 56 28
472.2.l.b 1568
472.2.m \(\chi_{472}(23, \cdot)\) None 0 28
472.2.p \(\chi_{472}(5, \cdot)\) 472.2.p.a 1624 28

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(472))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(472)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 2}\)