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Properties

Label 490.2.s
Level $490$
Weight $2$
Character orbit 490.s
Rep. character $\chi_{490}(13,\cdot)$
Character field $\Q(\zeta_{28})$
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.s (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{28})\)
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

\( 336 q + 28 q^{6} + 8 q^{7} + O(q^{10}) \) \( 336 q + 28 q^{6} + 8 q^{7} + 8 q^{11} + 44 q^{15} + 56 q^{16} + 28 q^{17} - 16 q^{21} - 20 q^{22} + 8 q^{23} - 8 q^{25} - 28 q^{26} - 8 q^{28} - 24 q^{30} + 8 q^{35} + 76 q^{36} - 24 q^{37} - 56 q^{41} - 112 q^{42} - 24 q^{43} + 112 q^{45} - 68 q^{46} - 84 q^{47} - 32 q^{50} - 80 q^{51} - 100 q^{53} + 84 q^{55} - 20 q^{56} + 92 q^{57} - 80 q^{58} - 112 q^{61} - 32 q^{67} + 52 q^{70} + 16 q^{71} - 84 q^{75} + 16 q^{77} - 80 q^{78} + 12 q^{81} + 140 q^{83} + 40 q^{85} - 8 q^{86} - 28 q^{87} - 8 q^{88} - 84 q^{90} + 124 q^{91} + 8 q^{92} + 20 q^{93} - 56 q^{95} - 32 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.s.a 490.s 245.s $336$ $3.913$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{28}]$

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

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