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Properties

Label 310.2.k
Level $310$
Weight $2$
Character orbit 310.k
Rep. character $\chi_{310}(129,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 310 = 2 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 310.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(310, [\chi])\).

Total New Old
Modular forms 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9} + O(q^{10}) \) \( 32 q - 32 q^{4} - 2 q^{5} + 4 q^{6} + 8 q^{9} - 4 q^{10} + 4 q^{11} + 8 q^{15} + 32 q^{16} - 8 q^{19} + 2 q^{20} + 16 q^{21} - 4 q^{24} + 22 q^{25} + 12 q^{26} - 8 q^{29} + 28 q^{30} + 12 q^{31} - 12 q^{34} - 32 q^{35} - 8 q^{36} - 64 q^{39} + 4 q^{40} - 16 q^{41} - 4 q^{44} - 24 q^{45} - 8 q^{46} + 20 q^{49} - 40 q^{51} + 8 q^{54} - 8 q^{55} + 16 q^{59} - 8 q^{60} - 40 q^{61} - 32 q^{64} - 6 q^{65} - 24 q^{66} + 36 q^{69} + 36 q^{70} + 48 q^{71} - 28 q^{74} + 8 q^{75} + 8 q^{76} + 4 q^{79} - 2 q^{80} - 32 q^{81} - 16 q^{84} - 84 q^{85} + 12 q^{86} + 72 q^{89} + 40 q^{90} + 24 q^{91} + 16 q^{94} - 48 q^{95} + 4 q^{96} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(310, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
310.2.k.a 310.k 155.j $32$ $2.475$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(310, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)