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Properties

Label 931.2.x
Level $931$
Weight $2$
Character orbit 931.x
Rep. character $\chi_{931}(226,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $378$
Newform subspaces $9$
Sturm bound $186$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.x (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 9 \)
Sturm bound: \(186\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(931, [\chi])\).

Total New Old
Modular forms 606 426 180
Cusp forms 510 378 132
Eisenstein series 96 48 48

Trace form

\( 378 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} + 12 q^{6} - 12 q^{8} + 3 q^{9} + O(q^{10}) \) \( 378 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} + 12 q^{6} - 12 q^{8} + 3 q^{9} - 15 q^{10} + 54 q^{12} + 12 q^{13} - 39 q^{15} - 9 q^{16} + 30 q^{18} - 6 q^{19} - 36 q^{22} + 3 q^{23} + 36 q^{24} + 3 q^{25} + 18 q^{26} - 30 q^{27} - 48 q^{29} - 3 q^{30} - 39 q^{31} - 6 q^{32} + 39 q^{33} + 24 q^{34} - 87 q^{36} - 6 q^{37} + 72 q^{38} + 24 q^{39} - 57 q^{40} + 30 q^{41} - 6 q^{43} - 96 q^{44} + 3 q^{45} - 12 q^{46} + 21 q^{47} + 21 q^{48} - 45 q^{50} + 3 q^{51} + 9 q^{52} - 3 q^{53} - 93 q^{54} + 27 q^{55} - 54 q^{57} + 78 q^{58} - 6 q^{59} - 228 q^{60} - 18 q^{61} + 27 q^{62} - 138 q^{64} - 21 q^{65} - 15 q^{66} + 84 q^{67} + 15 q^{68} - 42 q^{69} - 90 q^{71} - 18 q^{72} + 78 q^{73} - 3 q^{74} - 57 q^{75} - 42 q^{76} + 3 q^{78} + 15 q^{79} + 3 q^{80} - 60 q^{81} - 117 q^{82} + 18 q^{83} - 24 q^{85} + 54 q^{86} - 18 q^{87} + 45 q^{88} + 3 q^{89} + 48 q^{90} - 78 q^{92} + 39 q^{93} - 72 q^{94} - 117 q^{95} - 69 q^{96} - 3 q^{97} + 168 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(931, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
931.2.x.a 931.x 133.w $6$ $7.434$ \(\Q(\zeta_{18})\) None \(3\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}+\cdots\)
931.2.x.b 931.x 133.w $6$ $7.434$ \(\Q(\zeta_{18})\) None \(3\) \(3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}+\cdots\)
931.2.x.c 931.x 133.w $30$ $7.434$ None \(0\) \(-6\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{9}]$
931.2.x.d 931.x 133.w $30$ $7.434$ None \(0\) \(-6\) \(6\) \(0\) $\mathrm{SU}(2)[C_{9}]$
931.2.x.e 931.x 133.w $30$ $7.434$ None \(0\) \(6\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{9}]$
931.2.x.f 931.x 133.w $30$ $7.434$ None \(0\) \(6\) \(6\) \(0\) $\mathrm{SU}(2)[C_{9}]$
931.2.x.g 931.x 133.w $60$ $7.434$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
931.2.x.h 931.x 133.w $66$ $7.434$ None \(-3\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$
931.2.x.i 931.x 133.w $120$ $7.434$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(931, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(931, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)