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Properties

Label 310.2.w
Level $310$
Weight $2$
Character orbit 310.w
Rep. character $\chi_{310}(3,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $256$
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.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{60})\)
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 832 256 576
Cusp forms 704 256 448
Eisenstein series 128 0 128

Trace form

\( 256 q - 24 q^{7} + O(q^{10}) \) \( 256 q - 24 q^{7} - 8 q^{10} + 64 q^{16} + 4 q^{20} + 32 q^{21} - 52 q^{22} + 20 q^{23} + 20 q^{25} - 180 q^{27} + 4 q^{28} + 8 q^{31} - 44 q^{33} + 48 q^{35} + 128 q^{36} - 108 q^{37} - 52 q^{38} - 32 q^{41} + 8 q^{42} - 48 q^{43} - 28 q^{45} + 40 q^{46} + 20 q^{47} + 20 q^{48} - 48 q^{50} + 16 q^{51} + 28 q^{53} - 80 q^{55} - 24 q^{57} - 20 q^{60} + 20 q^{62} - 256 q^{63} - 8 q^{65} - 56 q^{66} + 4 q^{67} - 40 q^{70} + 88 q^{71} + 32 q^{73} - 32 q^{75} - 96 q^{76} + 20 q^{77} - 112 q^{78} + 48 q^{81} + 8 q^{82} - 108 q^{83} - 120 q^{85} - 24 q^{86} + 8 q^{87} - 108 q^{88} - 32 q^{90} - 80 q^{91} - 260 q^{93} + 64 q^{95} - 88 q^{97} - 112 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
310.2.w.a 310.w 155.x $256$ $2.475$ None 310.2.w.a \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{60}]$

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

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