Properties

Label 296.1
Level 296
Weight 1
Dimension 6
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 5472
Trace bound 1

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Defining parameters

Level: \( N \) = \( 296 = 2^{3} \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(5472\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(296))\).

Total New Old
Modular forms 242 76 166
Cusp forms 26 6 20
Eisenstein series 216 70 146

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 2 0

Trace form

\( 6 q - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{7} + 2 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{7} + 2 q^{9} - 2 q^{10} - 2 q^{11} - 2 q^{12} + 2 q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{23} + 2 q^{25} - 2 q^{26} - 4 q^{27} + 2 q^{29} - 4 q^{30} - 6 q^{33} + 2 q^{35} + 2 q^{36} - 2 q^{37} + 2 q^{39} - 2 q^{40} - 2 q^{41} + 2 q^{43} - 2 q^{44} - 2 q^{46} - 2 q^{47} - 2 q^{48} + 4 q^{49} - 2 q^{53} - 2 q^{55} - 2 q^{58} - 2 q^{62} + 4 q^{64} - 4 q^{65} - 2 q^{67} + 2 q^{69} + 2 q^{71} - 2 q^{73} + 4 q^{74} + 6 q^{75} + 6 q^{78} - 2 q^{81} + 6 q^{83} - 2 q^{87} + 4 q^{90} - 2 q^{91} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(296))\)

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
296.1.b \(\chi_{296}(295, \cdot)\) None 0 1
296.1.d \(\chi_{296}(223, \cdot)\) None 0 1
296.1.f \(\chi_{296}(75, \cdot)\) None 0 1
296.1.h \(\chi_{296}(147, \cdot)\) 296.1.h.a 2 1
296.1.h.b 2
296.1.k \(\chi_{296}(105, \cdot)\) 296.1.k.a 2 2
296.1.m \(\chi_{296}(117, \cdot)\) None 0 2
296.1.n \(\chi_{296}(11, \cdot)\) None 0 2
296.1.p \(\chi_{296}(195, \cdot)\) None 0 2
296.1.r \(\chi_{296}(47, \cdot)\) None 0 2
296.1.t \(\chi_{296}(159, \cdot)\) None 0 2
296.1.v \(\chi_{296}(29, \cdot)\) None 0 4
296.1.x \(\chi_{296}(97, \cdot)\) None 0 4
296.1.z \(\chi_{296}(3, \cdot)\) None 0 6
296.1.bb \(\chi_{296}(83, \cdot)\) None 0 6
296.1.bd \(\chi_{296}(95, \cdot)\) None 0 6
296.1.be \(\chi_{296}(7, \cdot)\) None 0 6
296.1.bg \(\chi_{296}(5, \cdot)\) None 0 12
296.1.bi \(\chi_{296}(17, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(296))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(296)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 2}\)