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Properties

Label 495.2.bl
Level $495$
Weight $2$
Character orbit 495.bl
Rep. character $\chi_{495}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $544$
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.bl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{30})\)
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 608 608 0
Cusp forms 544 544 0
Eisenstein series 64 64 0

Trace form

\( 544 q - 70 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{9} + O(q^{10}) \) \( 544 q - 70 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{9} - 24 q^{10} - 6 q^{11} + 10 q^{14} - 6 q^{15} + 42 q^{16} - 24 q^{19} - 9 q^{20} - 24 q^{21} - 48 q^{24} - 40 q^{26} - 22 q^{29} - 12 q^{30} - 12 q^{31} - 24 q^{34} - 22 q^{35} - 28 q^{36} + 92 q^{39} - 17 q^{40} + 26 q^{41} - 56 q^{44} - 100 q^{45} - 48 q^{46} - 50 q^{49} + 21 q^{50} + 32 q^{51} - 72 q^{54} - 38 q^{55} - 56 q^{56} + 32 q^{59} - 79 q^{60} - 6 q^{61} - 160 q^{66} - 64 q^{69} + 6 q^{70} - 76 q^{71} - 154 q^{74} + 21 q^{75} + 16 q^{76} - 42 q^{79} + 196 q^{80} - 50 q^{81} + 6 q^{84} - 13 q^{85} - 66 q^{86} + 56 q^{89} + 74 q^{90} + 68 q^{91} - 38 q^{94} - q^{95} + 40 q^{96} - 114 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bl.a 495.bl 495.al $544$ $3.953$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{30}]$