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Properties

Label 2960.1.fm
Level $2960$
Weight $1$
Character orbit 2960.fm
Rep. character $\chi_{2960}(1157,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4$
Newform subspaces $1$
Sturm bound $456$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2960.fm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2960 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(456\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 20 20 0
Cusp forms 4 4 0
Eisenstein series 16 16 0

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

\( 4 q + 2 q^{4} + 4 q^{6} - 2 q^{7} + O(q^{10}) \) \( 4 q + 2 q^{4} + 4 q^{6} - 2 q^{7} - 4 q^{10} + 4 q^{11} - 4 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{21} - 2 q^{22} + 4 q^{23} + 2 q^{24} + 2 q^{25} - 4 q^{26} + 2 q^{28} - 4 q^{31} + 2 q^{33} + 2 q^{35} - 2 q^{39} - 2 q^{40} - 2 q^{42} - 4 q^{43} + 2 q^{44} - 2 q^{46} - 2 q^{53} - 2 q^{54} - 2 q^{55} - 2 q^{56} + 2 q^{59} - 4 q^{60} + 2 q^{61} - 4 q^{64} + 2 q^{65} + 4 q^{66} + 2 q^{69} + 2 q^{70} + 4 q^{74} - 4 q^{77} + 2 q^{81} + 4 q^{82} - 4 q^{84} - 4 q^{88} + 2 q^{91} + 2 q^{92} - 2 q^{96} + 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2960.1.fm.a 2960.fm 2960.em $4$ $1.477$ \(\Q(\zeta_{12})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)