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Properties

Label 310.3.j
Level $310$
Weight $3$
Character orbit 310.j
Rep. character $\chi_{310}(161,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 310 = 2 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 310.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(310, [\chi])\).

Total New Old
Modular forms 200 40 160
Cusp forms 184 40 144
Eisenstein series 16 0 16

Trace form

\( 40 q + 12 q^{3} + 80 q^{4} - 12 q^{7} + 48 q^{9} + O(q^{10}) \) \( 40 q + 12 q^{3} + 80 q^{4} - 12 q^{7} + 48 q^{9} + 12 q^{11} + 24 q^{12} + 36 q^{13} - 8 q^{14} + 160 q^{16} + 60 q^{17} + 32 q^{18} + 84 q^{19} + 180 q^{21} + 72 q^{22} - 100 q^{25} - 96 q^{26} - 24 q^{28} - 80 q^{31} - 392 q^{33} - 48 q^{34} - 80 q^{35} + 96 q^{36} - 108 q^{37} + 16 q^{38} - 136 q^{39} + 44 q^{41} + 240 q^{42} - 348 q^{43} + 24 q^{44} + 40 q^{45} - 192 q^{47} + 48 q^{48} - 48 q^{49} + 328 q^{51} + 72 q^{52} - 180 q^{53} - 120 q^{55} - 16 q^{56} + 300 q^{57} - 28 q^{59} - 8 q^{62} + 472 q^{63} + 320 q^{64} + 256 q^{66} - 72 q^{67} + 120 q^{68} - 232 q^{69} - 60 q^{71} + 64 q^{72} - 276 q^{73} + 48 q^{74} - 60 q^{75} + 168 q^{76} - 480 q^{78} + 612 q^{79} - 108 q^{81} + 128 q^{82} - 60 q^{83} + 360 q^{84} + 96 q^{86} + 92 q^{87} + 144 q^{88} - 80 q^{90} - 220 q^{93} - 336 q^{94} + 240 q^{95} - 488 q^{97} - 208 q^{98} - 288 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(310, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
310.3.j.a 310.j 31.e $40$ $8.447$ None \(0\) \(12\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(310, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(310, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)