Properties

Label 310.2.b
Level $310$
Weight $2$
Character orbit 310.b
Rep. character $\chi_{310}(249,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $96$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 310 = 2 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 310.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 52 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

Trace form

\( 16 q - 16 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{9} + O(q^{10}) \) \( 16 q - 16 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{15} + 16 q^{16} - 16 q^{19} + 4 q^{20} + 8 q^{21} + 4 q^{24} + 8 q^{25} - 12 q^{26} + 20 q^{29} + 8 q^{30} + 8 q^{35} + 8 q^{36} - 32 q^{39} - 4 q^{40} - 8 q^{41} + 4 q^{44} + 12 q^{45} - 16 q^{46} - 32 q^{49} - 56 q^{51} + 40 q^{54} + 20 q^{55} + 8 q^{59} - 4 q^{60} + 4 q^{61} - 16 q^{64} + 12 q^{65} + 24 q^{66} + 4 q^{74} - 32 q^{75} + 16 q^{76} + 56 q^{79} - 4 q^{80} + 56 q^{81} - 8 q^{84} + 12 q^{85} - 36 q^{86} - 28 q^{90} - 48 q^{91} - 16 q^{94} - 4 q^{96} + 44 q^{99} + O(q^{100}) \)

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.b.a 310.b 5.b $8$ $2.475$ 8.0.619810816.2 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
310.2.b.b 310.b 5.b $8$ $2.475$ 8.0.2058981376.2 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+\beta _{6}q^{3}-q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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