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Properties

Label 57.1
Level 57
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 240
Trace bound 0

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Defining parameters

Level: \( N \) = \( 57 = 3 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(57))\).

Total New Old
Modular forms 38 18 20
Cusp forms 2 2 0
Eisenstein series 36 16 20

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)

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
57.1.b \(\chi_{57}(20, \cdot)\) None 0 1
57.1.c \(\chi_{57}(37, \cdot)\) None 0 1
57.1.g \(\chi_{57}(31, \cdot)\) None 0 2
57.1.h \(\chi_{57}(11, \cdot)\) 57.1.h.a 2 2
57.1.k \(\chi_{57}(10, \cdot)\) None 0 6
57.1.l \(\chi_{57}(5, \cdot)\) None 0 6