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Properties

Label 310.2.e
Level $310$
Weight $2$
Character orbit 310.e
Rep. character $\chi_{310}(191,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $4$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 310 = 2 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 310.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 104 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

Trace form

\( 24 q + 24 q^{4} - 4 q^{7} - 16 q^{9} + O(q^{10}) \) \( 24 q + 24 q^{4} - 4 q^{7} - 16 q^{9} - 4 q^{11} + 20 q^{13} - 4 q^{14} + 24 q^{16} + 12 q^{17} + 16 q^{18} + 8 q^{19} - 20 q^{21} - 8 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 4 q^{28} - 8 q^{29} - 8 q^{30} - 20 q^{31} + 8 q^{33} - 4 q^{34} - 16 q^{35} - 16 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{39} - 4 q^{41} + 24 q^{43} - 4 q^{44} + 8 q^{45} + 8 q^{46} - 8 q^{47} - 20 q^{49} + 48 q^{51} + 20 q^{52} - 48 q^{54} - 4 q^{55} - 4 q^{56} - 4 q^{57} - 16 q^{58} + 8 q^{59} + 24 q^{61} + 12 q^{62} - 24 q^{63} + 24 q^{64} + 8 q^{65} + 24 q^{66} - 4 q^{67} + 12 q^{68} + 4 q^{69} - 8 q^{71} + 16 q^{72} - 4 q^{73} + 4 q^{74} + 8 q^{76} - 104 q^{77} - 32 q^{78} - 20 q^{79} - 60 q^{81} - 16 q^{82} - 20 q^{84} - 16 q^{86} - 40 q^{87} - 72 q^{89} - 8 q^{90} - 8 q^{91} - 8 q^{92} + 48 q^{93} - 32 q^{94} - 16 q^{95} - 24 q^{97} + 24 q^{98} - 32 q^{99} + O(q^{100}) \)

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.e.a 310.e 31.c $6$ $2.475$ 6.0.309123.1 None \(-6\) \(-1\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{2}q^{6}+\cdots\)
310.2.e.b 310.e 31.c $6$ $2.475$ 6.0.49572675.1 None \(-6\) \(1\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
310.2.e.c 310.e 31.c $6$ $2.475$ 6.0.309123.1 None \(6\) \(-1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(\beta _{1}-\beta _{5})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
310.2.e.d 310.e 31.c $6$ $2.475$ 6.0.771147.1 None \(6\) \(1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+\beta _{4}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)