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Properties

Label 471.4
Level 471
Weight 4
Dimension 18330
Nonzero newspaces 12
Sturm bound 65728
Trace bound 1

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Defining parameters

Level: \( N \) = \( 471 = 3 \cdot 157 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(65728\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(471))\).

Total New Old
Modular forms 24960 18642 6318
Cusp forms 24336 18330 6006
Eisenstein series 624 312 312

Trace form

\( 18330 q - 78 q^{3} - 156 q^{4} - 78 q^{6} - 156 q^{7} - 78 q^{9} + O(q^{10}) \) \( 18330 q - 78 q^{3} - 156 q^{4} - 78 q^{6} - 156 q^{7} - 78 q^{9} - 156 q^{10} - 78 q^{12} - 156 q^{13} - 78 q^{15} - 156 q^{16} - 78 q^{18} - 156 q^{19} - 78 q^{21} - 156 q^{22} - 78 q^{24} - 156 q^{25} - 78 q^{27} - 156 q^{28} - 78 q^{30} - 156 q^{31} - 78 q^{33} - 156 q^{34} - 78 q^{36} - 156 q^{37} - 78 q^{39} - 156 q^{40} - 78 q^{42} - 156 q^{43} - 78 q^{45} - 156 q^{46} - 78 q^{48} - 156 q^{49} - 78 q^{51} - 156 q^{52} - 78 q^{54} - 156 q^{55} - 78 q^{57} - 156 q^{58} - 78 q^{60} - 156 q^{61} - 78 q^{63} - 156 q^{64} - 78 q^{66} - 156 q^{67} - 78 q^{69} - 156 q^{70} - 78 q^{72} - 156 q^{73} - 78 q^{75} - 156 q^{76} - 78 q^{78} - 156 q^{79} - 78 q^{81} - 156 q^{82} - 78 q^{84} - 156 q^{85} - 78 q^{87} - 156 q^{88} - 78 q^{90} - 156 q^{91} - 78 q^{93} - 156 q^{94} - 78 q^{96} - 156 q^{97} - 78 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(471))\)

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
471.4.a \(\chi_{471}(1, \cdot)\) 471.4.a.a 14 1
471.4.a.b 17
471.4.a.c 22
471.4.a.d 25
471.4.b \(\chi_{471}(313, \cdot)\) 471.4.b.a 40 1
471.4.b.b 40
471.4.e \(\chi_{471}(169, \cdot)\) n/a 156 2
471.4.f \(\chi_{471}(185, \cdot)\) n/a 312 2
471.4.h \(\chi_{471}(13, \cdot)\) n/a 160 2
471.4.l \(\chi_{471}(50, \cdot)\) n/a 624 4
471.4.m \(\chi_{471}(16, \cdot)\) n/a 936 12
471.4.p \(\chi_{471}(4, \cdot)\) n/a 960 12
471.4.q \(\chi_{471}(19, \cdot)\) n/a 1872 24
471.4.s \(\chi_{471}(2, \cdot)\) n/a 3744 24
471.4.v \(\chi_{471}(10, \cdot)\) n/a 1920 24
471.4.w \(\chi_{471}(5, \cdot)\) n/a 7488 48

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(471))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(471)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(157))\)\(^{\oplus 2}\)