Properties

Label 52.1
Level 52
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 168
Trace bound 0

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Defining parameters

Level: \( N \) = \( 52 = 2^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(52))\).

Total New Old
Modular forms 32 12 20
Cusp forms 2 2 0
Eisenstein series 30 10 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

\( 2q - q^{2} - q^{4} - 2q^{5} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - 2q^{5} + 2q^{8} - q^{9} + q^{10} - q^{13} - q^{16} + q^{17} + 2q^{18} + q^{20} - q^{26} + q^{29} - q^{32} - 2q^{34} - q^{36} + q^{37} - 2q^{40} + q^{41} + q^{45} - q^{49} + 2q^{52} - 2q^{53} + q^{58} + q^{61} + 2q^{64} + q^{65} + q^{68} - q^{72} - 2q^{73} + q^{74} + q^{80} - q^{81} + q^{82} - q^{85} - 2q^{89} - 2q^{90} - 2q^{97} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)

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
52.1.b \(\chi_{52}(51, \cdot)\) None 0 1
52.1.c \(\chi_{52}(27, \cdot)\) None 0 1
52.1.g \(\chi_{52}(5, \cdot)\) None 0 2
52.1.i \(\chi_{52}(23, \cdot)\) None 0 2
52.1.j \(\chi_{52}(3, \cdot)\) 52.1.j.a 2 2
52.1.k \(\chi_{52}(33, \cdot)\) None 0 4