Properties

Label 471.1
Level 471
Weight 1
Dimension 31
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 16432
Trace bound 4

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Defining parameters

Level: \( N \) = \( 471 = 3 \cdot 157 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(16432\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(471))\).

Total New Old
Modular forms 343 185 158
Cusp forms 31 31 0
Eisenstein series 312 154 158

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 31 0 0 0

Trace form

\( 31q - 3q^{3} + 5q^{4} - 2q^{7} + 5q^{9} + O(q^{10}) \) \( 31q - 3q^{3} + 5q^{4} - 2q^{7} + 5q^{9} - 4q^{10} - 3q^{12} - 6q^{13} + q^{16} - 2q^{19} - 2q^{21} + 5q^{25} - 3q^{27} - 2q^{28} - 4q^{30} - 2q^{31} + 5q^{36} - 2q^{37} - 6q^{39} - 8q^{40} - 2q^{43} - 4q^{46} - 7q^{48} + 3q^{49} - 6q^{52} - 2q^{57} - 4q^{58} - 2q^{61} - 2q^{63} + q^{64} - 6q^{67} - 2q^{73} - 3q^{75} - 10q^{76} - 2q^{79} + 5q^{81} - 4q^{82} - 2q^{84} - 4q^{90} - 4q^{91} - 2q^{93} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(471))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
471.1.c \(\chi_{471}(158, \cdot)\) None 0 1
471.1.d \(\chi_{471}(470, \cdot)\) 471.1.d.a 1 1
471.1.d.b 2
471.1.d.c 4
471.1.g \(\chi_{471}(28, \cdot)\) None 0 2
471.1.i \(\chi_{471}(326, \cdot)\) None 0 2
471.1.j \(\chi_{471}(170, \cdot)\) None 0 2
471.1.k \(\chi_{471}(22, \cdot)\) None 0 4
471.1.n \(\chi_{471}(56, \cdot)\) 471.1.n.a 12 12
471.1.o \(\chi_{471}(14, \cdot)\) 471.1.o.a 12 12
471.1.r \(\chi_{471}(7, \cdot)\) None 0 24
471.1.t \(\chi_{471}(44, \cdot)\) None 0 24
471.1.u \(\chi_{471}(11, \cdot)\) None 0 24
471.1.x \(\chi_{471}(34, \cdot)\) None 0 48