Properties

Label 310.2.n
Level $310$
Weight $2$
Character orbit 310.n
Rep. character $\chi_{310}(39,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $64$
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.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{10})\)
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 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

Trace form

\( 64q + 16q^{4} + 4q^{5} - 16q^{6} + 8q^{9} + O(q^{10}) \) \( 64q + 16q^{4} + 4q^{5} - 16q^{6} + 8q^{9} - 4q^{10} + 4q^{11} - 14q^{15} - 16q^{16} + 16q^{19} - 4q^{20} + 32q^{21} - 4q^{24} - 8q^{25} - 48q^{26} - 40q^{29} - 8q^{30} - 60q^{31} - 20q^{34} - 8q^{35} + 72q^{36} - 8q^{39} - 6q^{40} + 28q^{41} - 4q^{44} - 22q^{45} + 36q^{46} + 32q^{49} + 20q^{50} - 4q^{51} - 40q^{54} + 32q^{59} + 14q^{60} - 64q^{61} + 16q^{64} + 48q^{65} - 4q^{66} - 20q^{70} - 20q^{71} - 4q^{74} + 62q^{75} + 24q^{76} - 116q^{79} - 6q^{80} - 116q^{81} + 8q^{84} + 8q^{85} - 24q^{86} + 60q^{89} - 82q^{90} + 28q^{91} + 16q^{94} - 90q^{95} + 4q^{96} + 16q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
310.2.n.a \(64\) \(2.475\) None \(0\) \(0\) \(4\) \(0\)

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

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