Properties

Label 2960.1.cj
Level $2960$
Weight $1$
Character orbit 2960.cj
Rep. character $\chi_{2960}(2769,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $456$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2960.cj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(456\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2960, [\chi])\).

Total New Old
Modular forms 40 8 32
Cusp forms 16 4 12
Eisenstein series 24 4 20

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

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

Trace form

\( 4q + 2q^{5} + O(q^{10}) \) \( 4q + 2q^{5} + 2q^{15} - 4q^{31} + 2q^{35} - 2q^{55} - 4q^{61} + 4q^{71} + 4q^{75} - 4q^{79} - 4q^{81} - 4q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2960, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2960.1.cj.a \(2\) \(1.477\) \(\Q(\sqrt{-1}) \) \(S_{4}\) None None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+iq^{5}-iq^{7}+iq^{11}-iq^{15}+\cdots\)
2960.1.cj.b \(2\) \(1.477\) \(\Q(\sqrt{-1}) \) \(S_{4}\) None None \(0\) \(2\) \(2\) \(0\) \(q+q^{3}+q^{5}+iq^{7}+iq^{11}+q^{15}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2960, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2960, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(740, [\chi])\)\(^{\oplus 3}\)