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Properties

Label 560.2.bj
Level $560$
Weight $2$
Character orbit 560.bj
Rep. character $\chi_{560}(97,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
Newform subspaces $4$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(7\)
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 52 164
Cusp forms 168 44 124
Eisenstein series 48 8 40

Trace form

\( 44 q + 2 q^{7} + O(q^{10}) \) \( 44 q + 2 q^{7} + 8 q^{11} + 4 q^{15} + 4 q^{21} + 28 q^{23} - 4 q^{25} - 10 q^{35} - 4 q^{37} + 4 q^{43} + 32 q^{51} - 4 q^{53} - 32 q^{57} - 54 q^{63} - 20 q^{65} - 20 q^{67} + 64 q^{71} - 16 q^{77} - 4 q^{81} - 4 q^{85} + 36 q^{91} + 24 q^{93} + 24 q^{95} + O(q^{100}) \)

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.bj.a 560.bj 35.f $4$ $4.472$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
560.2.bj.b 560.bj 35.f $8$ $4.472$ 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(\beta _{2}-\beta _{6})q^{5}+(-\beta _{4}+\beta _{6}+\cdots)q^{7}+\cdots\)
560.2.bj.c 560.bj 35.f $8$ $4.472$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{16}+\zeta_{16}^{3})q^{3}+(-\zeta_{16}-2\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
560.2.bj.d 560.bj 35.f $24$ $4.472$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)