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Properties

Label 931.2.bj
Level $931$
Weight $2$
Character orbit 931.bj
Rep. character $\chi_{931}(117,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $378$
Newform subspaces $3$
Sturm bound $186$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.bj (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 3 \)
Sturm bound: \(186\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

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

\( 378 q + 3 q^{2} + 9 q^{3} + 3 q^{4} + 9 q^{5} - 36 q^{8} + 3 q^{9} + O(q^{10}) \) \( 378 q + 3 q^{2} + 9 q^{3} + 3 q^{4} + 9 q^{5} - 36 q^{8} + 3 q^{9} + 9 q^{10} + 12 q^{11} - 6 q^{12} + 30 q^{13} - 57 q^{15} + 15 q^{16} - 18 q^{17} - 72 q^{18} - 12 q^{19} - 48 q^{22} + 3 q^{23} + 36 q^{24} + 51 q^{25} - 12 q^{27} - 24 q^{29} - 3 q^{30} + 9 q^{31} - 60 q^{32} + 9 q^{33} + 36 q^{34} - 63 q^{36} + 36 q^{37} - 18 q^{38} - 12 q^{39} - 9 q^{40} - 54 q^{41} - 90 q^{43} - 162 q^{44} + 27 q^{45} - 45 q^{47} - 63 q^{48} + 9 q^{50} + 3 q^{51} - 57 q^{52} - 39 q^{53} + 9 q^{54} + 45 q^{55} + 6 q^{57} - 66 q^{58} - 36 q^{59} - 102 q^{60} + 42 q^{61} + 45 q^{62} + 114 q^{64} - 45 q^{65} - 9 q^{66} - 12 q^{67} + 9 q^{68} - 54 q^{71} - 108 q^{72} - 60 q^{73} - 63 q^{74} + 21 q^{75} - 54 q^{76} - 27 q^{78} + 87 q^{79} + 45 q^{80} - 12 q^{81} + 9 q^{82} - 36 q^{83} + 24 q^{85} + 60 q^{86} + 9 q^{88} + 9 q^{89} + 18 q^{90} - 138 q^{92} + 39 q^{93} - 90 q^{94} + 75 q^{95} - 63 q^{96} + 27 q^{97} - 132 q^{99} + O(q^{100}) \)

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.bj.a 931.bj 133.af $66$ $7.434$ None \(-3\) \(9\) \(9\) \(0\) $\mathrm{SU}(2)[C_{18}]$
931.2.bj.b 931.bj 133.af $72$ $7.434$ None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
931.2.bj.c 931.bj 133.af $240$ $7.434$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

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

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