Properties

Label 2960.1.o
Level $2960$
Weight $1$
Character orbit 2960.o
Rep. character $\chi_{2960}(2959,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $456$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2960.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 740 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(456\)
Trace bound: \(5\)

Dimensions

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

Total New Old
Modular forms 38 8 30
Cusp forms 26 8 18
Eisenstein series 12 0 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 8 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{9} + 8 q^{25} + 8 q^{49} + 8 q^{81} + O(q^{100}) \)

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.o.a \(4\) \(1.477\) \(\Q(\zeta_{16})^+\) \(D_{8}\) \(\Q(\sqrt{-185}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+(1+\beta _{2})q^{9}+\cdots\)
2960.1.o.b \(4\) \(1.477\) \(\Q(\zeta_{16})^+\) \(D_{8}\) \(\Q(\sqrt{-185}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{1}q^{3}+q^{5}+\beta _{3}q^{7}+(1+\beta _{2})q^{9}+\cdots\)

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

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