Properties

Label 495.2.bv
Level $495$
Weight $2$
Character orbit 495.bv
Rep. character $\chi_{495}(38,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1088$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(495, [\chi])\).

Total New Old
Modular forms 1216 1216 0
Cusp forms 1088 1088 0
Eisenstein series 128 128 0

Trace form

\( 1088 q - 18 q^{2} - 10 q^{3} - 18 q^{5} - 24 q^{6} - 6 q^{7} + O(q^{10}) \) \( 1088 q - 18 q^{2} - 10 q^{3} - 18 q^{5} - 24 q^{6} - 6 q^{7} - 64 q^{10} - 60 q^{11} + 20 q^{12} - 6 q^{13} - 4 q^{15} - 124 q^{16} - 20 q^{18} - 42 q^{20} - 72 q^{21} - 48 q^{23} - 12 q^{25} - 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} - 62 q^{33} + 88 q^{36} - 36 q^{37} - 150 q^{38} + 18 q^{40} - 36 q^{41} + 4 q^{42} - 16 q^{43} - 20 q^{45} - 48 q^{46} - 42 q^{47} - 64 q^{48} + 78 q^{50} - 64 q^{51} + 18 q^{52} - 12 q^{55} - 264 q^{56} - 84 q^{57} - 58 q^{58} - 136 q^{60} - 12 q^{61} - 4 q^{63} - 48 q^{65} - 76 q^{66} + 8 q^{67} + 30 q^{68} - 46 q^{70} - 14 q^{72} - 24 q^{73} + 28 q^{75} - 64 q^{76} - 264 q^{77} - 104 q^{78} + 44 q^{81} - 8 q^{82} + 102 q^{83} - 6 q^{85} + 180 q^{86} - 108 q^{87} + 92 q^{88} + 356 q^{90} - 120 q^{91} + 234 q^{92} - 70 q^{93} - 78 q^{95} + 100 q^{96} - 12 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
495.2.bv.a 495.bv 495.av $1088$ $3.953$ None \(-18\) \(-10\) \(-18\) \(-6\) $\mathrm{SU}(2)[C_{60}]$