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Properties

Label 560.2.bs
Level $560$
Weight $2$
Character orbit 560.bs
Rep. character $\chi_{560}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $3$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(560, [\chi])\).

Total New Old
Modular forms 216 32 184
Cusp forms 168 32 136
Eisenstein series 48 0 48

Trace form

\( 32 q - 16 q^{9} + O(q^{10}) \) \( 32 q - 16 q^{9} + 4 q^{21} + 16 q^{25} + 24 q^{29} + 8 q^{37} - 36 q^{45} - 16 q^{49} - 24 q^{53} - 16 q^{57} - 72 q^{61} - 12 q^{65} + 24 q^{73} + 120 q^{77} - 4 q^{81} + 36 q^{89} + 40 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
560.2.bs.a 560.bs 28.f $8$ $4.472$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{3}+(\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
560.2.bs.b 560.bs 28.f $12$ $4.472$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{3}-\beta _{4}-\beta _{8})q^{3}-\beta _{4}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
560.2.bs.c 560.bs 28.f $12$ $4.472$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}+\beta _{4}+\beta _{8})q^{3}-\beta _{4}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)