Properties

Label 156.1
Level 156
Weight 1
Dimension 4
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 1344
Trace bound 3

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Defining parameters

Level: \( N \) = \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(1344\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(156))\).

Total New Old
Modular forms 131 28 103
Cusp forms 11 4 7
Eisenstein series 120 24 96

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q - 2q^{7} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{7} - 2q^{9} - 2q^{19} - 2q^{21} - 2q^{31} - 2q^{37} + 4q^{39} + 2q^{43} + 2q^{49} + 4q^{57} + 4q^{63} + 4q^{67} - 2q^{73} - 2q^{75} - 2q^{81} - 2q^{91} - 2q^{93} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)

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
156.1.d \(\chi_{156}(53, \cdot)\) None 0 1
156.1.e \(\chi_{156}(103, \cdot)\) None 0 1
156.1.f \(\chi_{156}(79, \cdot)\) None 0 1
156.1.g \(\chi_{156}(77, \cdot)\) None 0 1
156.1.j \(\chi_{156}(73, \cdot)\) None 0 2
156.1.l \(\chi_{156}(47, \cdot)\) None 0 2
156.1.n \(\chi_{156}(43, \cdot)\) None 0 2
156.1.o \(\chi_{156}(29, \cdot)\) 156.1.o.a 2 2
156.1.s \(\chi_{156}(17, \cdot)\) 156.1.s.a 2 2
156.1.t \(\chi_{156}(55, \cdot)\) None 0 2
156.1.v \(\chi_{156}(11, \cdot)\) None 0 4
156.1.x \(\chi_{156}(37, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(156))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(156)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)