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Properties

Label 310.2.t
Level $310$
Weight $2$
Character orbit 310.t
Rep. character $\chi_{310}(9,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $128$
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.t (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{30})\)
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 416 128 288
Cusp forms 352 128 224
Eisenstein series 64 0 64

Trace form

\( 128 q + 32 q^{4} + 2 q^{5} + 16 q^{6} - 8 q^{9} + O(q^{10}) \) \( 128 q + 32 q^{4} + 2 q^{5} + 16 q^{6} - 8 q^{9} + 4 q^{10} - 4 q^{11} + 2 q^{15} - 32 q^{16} + 8 q^{19} - 2 q^{20} - 56 q^{21} + 4 q^{24} - 22 q^{25} + 48 q^{26} - 32 q^{29} - 28 q^{30} + 48 q^{31} - 28 q^{34} + 32 q^{35} - 72 q^{36} - 16 q^{39} + 6 q^{40} - 4 q^{41} + 4 q^{44} + 34 q^{45} - 12 q^{46} - 20 q^{49} - 20 q^{50} - 80 q^{51} - 8 q^{54} + 48 q^{55} - 56 q^{59} - 2 q^{60} - 80 q^{61} + 32 q^{64} + 36 q^{65} + 4 q^{66} - 36 q^{69} - 16 q^{70} - 148 q^{71} + 28 q^{74} + 22 q^{75} - 48 q^{76} + 56 q^{79} - 18 q^{80} + 92 q^{81} + 16 q^{84} - 56 q^{85} + 48 q^{86} - 132 q^{89} - 110 q^{90} - 4 q^{91} - 16 q^{94} - 102 q^{95} - 4 q^{96} - 124 q^{99} + O(q^{100}) \)

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.t.a 310.t 155.u $128$ $2.475$ None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{30}]$

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

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