Properties

Label 76.1
Level 76
Weight 1
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 360
Trace bound 0

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Defining parameters

Level: \( N \) = \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(76))\).

Total New Old
Modular forms 46 17 29
Cusp forms 1 1 0
Eisenstein series 45 16 29

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{5} - q^{7} + q^{9} + O(q^{10}) \) \( q - q^{5} - q^{7} + q^{9} - q^{11} - q^{17} + q^{19} + 2q^{23} + q^{35} - q^{43} - q^{45} - q^{47} + q^{55} - q^{61} - q^{63} - q^{73} + q^{77} + q^{81} + 2q^{83} + q^{85} - q^{95} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)

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
76.1.b \(\chi_{76}(39, \cdot)\) None 0 1
76.1.c \(\chi_{76}(37, \cdot)\) 76.1.c.a 1 1
76.1.g \(\chi_{76}(7, \cdot)\) None 0 2
76.1.h \(\chi_{76}(65, \cdot)\) None 0 2
76.1.j \(\chi_{76}(13, \cdot)\) None 0 6
76.1.l \(\chi_{76}(23, \cdot)\) None 0 6