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Properties

Label 660.2.n
Level $660$
Weight $2$
Character orbit 660.n
Rep. character $\chi_{660}(329,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $3$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 660.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\), \(23\)

Dimensions

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

Total New Old
Modular forms 156 24 132
Cusp forms 132 24 108
Eisenstein series 24 0 24

Trace form

\( 24 q - 6 q^{9} + O(q^{10}) \) \( 24 q - 6 q^{9} - q^{15} - 14 q^{25} - 12 q^{31} - 15 q^{45} + 56 q^{49} + 26 q^{55} - 22 q^{69} - 17 q^{75} - 62 q^{81} + 32 q^{91} + 10 q^{99} + O(q^{100}) \)

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.n.a 660.n 165.d $4$ $5.270$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(3\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
660.2.n.b 660.n 165.d $4$ $5.270$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(-3\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
660.2.n.c 660.n 165.d $16$ $5.270$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{3}+(\beta _{2}-\beta _{4})q^{5}+\beta _{9}q^{7}+(-1+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(660, [\chi]) \cong \)