Properties

Label 560.2.bw
Level $560$
Weight $2$
Character orbit 560.bw
Rep. character $\chi_{560}(289,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $6$
Sturm bound $192$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(9\)
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

\( 44 q - q^{5} + 16 q^{9} + O(q^{10}) \) \( 44 q - q^{5} + 16 q^{9} + 2 q^{11} + 10 q^{15} + 14 q^{19} - 14 q^{21} - 5 q^{25} + 14 q^{31} + 13 q^{35} - 16 q^{39} - 16 q^{41} + 12 q^{45} - 20 q^{49} + 26 q^{51} - 18 q^{55} + 30 q^{59} - 2 q^{61} - 4 q^{65} - 36 q^{69} - 32 q^{71} + 25 q^{75} + 26 q^{79} + 10 q^{81} - 30 q^{85} + 10 q^{89} - 80 q^{91} + 27 q^{95} + 8 q^{99} + O(q^{100}) \)

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.bw.a 560.bw 35.j $4$ $4.472$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(-6\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)
560.2.bw.b 560.bw 35.j $4$ $4.472$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\cdots\)
560.2.bw.c 560.bw 35.j $4$ $4.472$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+3\zeta_{12}q^{3}+(2\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
560.2.bw.d 560.bw 35.j $4$ $4.472$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}+2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+(-2\zeta_{12}+\cdots)q^{7}+\cdots\)
560.2.bw.e 560.bw 35.j $4$ $4.472$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(6\) \(1\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots\)
560.2.bw.f 560.bw 35.j $24$ $4.472$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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