Properties

Label 490.2.t
Level $490$
Weight $2$
Character orbit 490.t
Rep. character $\chi_{490}(9,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $336$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.t (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(490, [\chi])\).

Total New Old
Modular forms 1056 336 720
Cusp forms 960 336 624
Eisenstein series 96 0 96

Trace form

\( 336 q - 28 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{9} + O(q^{10}) \) \( 336 q - 28 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{9} - 2 q^{10} + 30 q^{11} + 2 q^{14} + 2 q^{15} + 28 q^{16} - 14 q^{19} + 10 q^{20} - 6 q^{21} + 6 q^{24} - 28 q^{26} + 2 q^{29} - 6 q^{30} + 16 q^{31} - 16 q^{34} - 26 q^{35} - 66 q^{36} - 124 q^{39} - 26 q^{40} + 56 q^{41} - 30 q^{44} - 150 q^{45} + 76 q^{46} - 86 q^{49} + 8 q^{50} + 116 q^{51} - 66 q^{54} - 102 q^{55} + 26 q^{56} - 38 q^{59} - 20 q^{60} + 106 q^{61} + 56 q^{64} + 2 q^{65} + 12 q^{69} - 12 q^{70} + 68 q^{71} + 16 q^{74} - 24 q^{75} + 28 q^{76} - 2 q^{80} + 38 q^{81} - 60 q^{84} + 48 q^{85} + 94 q^{86} - 130 q^{89} - 102 q^{90} - 90 q^{91} + 68 q^{94} - 116 q^{95} - 6 q^{96} + 212 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(490, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
490.2.t.a 490.t 245.t $336$ $3.913$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{42}]$

Decomposition of \(S_{2}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(490, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)