Properties

Label 1960.1.bi
Level $1960$
Weight $1$
Character orbit 1960.bi
Rep. character $\chi_{1960}(459,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $336$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1960.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(336\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1960, [\chi])\).

Total New Old
Modular forms 44 20 24
Cusp forms 12 4 8
Eisenstein series 32 16 16

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

\( 4q - 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{4} - 2q^{9} + 2q^{10} + 2q^{11} - 2q^{16} - 2q^{19} - 2q^{25} - 2q^{26} + 4q^{36} + 2q^{40} + 4q^{41} + 2q^{44} + 2q^{46} + 4q^{59} + 4q^{64} + 2q^{65} + 2q^{74} + 4q^{76} - 2q^{81} + 4q^{89} - 4q^{90} - 2q^{94} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1960, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1960.1.bi.a \(2\) \(0.978\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-10}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{8}-\zeta_{6}q^{9}+\cdots\)
1960.1.bi.b \(2\) \(0.978\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-10}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{8}-\zeta_{6}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1960, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1960, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)