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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

\( 336 q - 28 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{9} - 2 q^{10} + 30 q^{11} + 2 q^{14} + 2 q^{15} + 28 q^{16} - 14 q^{19} + 10 q^{20} - 6 q^{21} + 6 q^{24} - 28 q^{26} + 2 q^{29} - 6 q^{30} + 16 q^{31} - 16 q^{34}+ \cdots + 212 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist 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 490.2.t.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{42}]$

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

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