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Properties

Label 660.2.bs
Level $660$
Weight $2$
Character orbit 660.bs
Rep. character $\chi_{660}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $192$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 660.bs (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(660, [\chi])\).

Total New Old
Modular forms 1248 192 1056
Cusp forms 1056 192 864
Eisenstein series 192 0 192

Trace form

\( 192 q - 2 q^{3} + 8 q^{7} + O(q^{10}) \) \( 192 q - 2 q^{3} + 8 q^{7} + 8 q^{13} + 4 q^{15} + 8 q^{21} + 12 q^{25} + 4 q^{27} - 16 q^{31} + 28 q^{33} - 4 q^{37} + 64 q^{43} + 32 q^{45} + 64 q^{51} + 28 q^{55} - 48 q^{57} + 24 q^{61} + 20 q^{63} - 16 q^{67} - 20 q^{73} - 52 q^{75} + 32 q^{85} - 32 q^{87} + 24 q^{91} - 62 q^{93} - 20 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(660, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
660.2.bs.a 660.bs 165.v $192$ $5.270$ None \(0\) \(-2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(660, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(660, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)