Properties

Label 676.1
Level 676
Weight 1
Dimension 46
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 28392
Trace bound 4

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Defining parameters

Level: \( N \) = \( 676 = 2^{2} \cdot 13^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(28392\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(676))\).

Total New Old
Modular forms 620 251 369
Cusp forms 50 46 4
Eisenstein series 570 205 365

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 46 0 0 0

Trace form

\( 46 q + q^{2} + q^{4} + 2 q^{5} - 5 q^{8} + q^{9} + O(q^{10}) \) \( 46 q + q^{2} + q^{4} + 2 q^{5} - 5 q^{8} + q^{9} - 4 q^{10} + q^{16} - 4 q^{17} - 5 q^{18} - 4 q^{20} - 3 q^{25} - 4 q^{29} + q^{32} + 2 q^{34} + q^{36} - 4 q^{37} - 10 q^{40} - 4 q^{41} - 4 q^{45} + q^{49} - 3 q^{50} - 3 q^{52} - 10 q^{53} - 4 q^{58} - 4 q^{61} - 5 q^{64} - 3 q^{65} - 4 q^{68} + q^{72} + 2 q^{73} - 4 q^{74} - 4 q^{80} + q^{81} - 4 q^{82} - 2 q^{85} + 2 q^{89} + 2 q^{90} + 2 q^{97} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(676))\)

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
676.1.b \(\chi_{676}(675, \cdot)\) 676.1.b.a 2 1
676.1.c \(\chi_{676}(339, \cdot)\) 676.1.c.a 1 1
676.1.c.b 1
676.1.g \(\chi_{676}(437, \cdot)\) None 0 2
676.1.i \(\chi_{676}(23, \cdot)\) 676.1.i.a 4 2
676.1.j \(\chi_{676}(191, \cdot)\) 676.1.j.a 2 2
676.1.k \(\chi_{676}(89, \cdot)\) None 0 4
676.1.o \(\chi_{676}(27, \cdot)\) 676.1.o.a 12 12
676.1.p \(\chi_{676}(51, \cdot)\) None 0 12
676.1.r \(\chi_{676}(5, \cdot)\) None 0 24
676.1.t \(\chi_{676}(3, \cdot)\) 676.1.t.a 24 24
676.1.u \(\chi_{676}(43, \cdot)\) None 0 24
676.1.x \(\chi_{676}(33, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(676))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(676)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)