Properties

Label 560.2.q
Level $560$
Weight $2$
Character orbit 560.q
Rep. character $\chi_{560}(81,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $12$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

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

\( 32 q - 4 q^{3} - 4 q^{7} - 16 q^{9} + O(q^{10}) \) \( 32 q - 4 q^{3} - 4 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{19} + 4 q^{21} + 4 q^{23} - 16 q^{25} + 32 q^{27} + 24 q^{29} + 16 q^{31} - 8 q^{37} - 8 q^{39} + 8 q^{41} - 40 q^{43} - 4 q^{45} + 20 q^{47} - 16 q^{49} - 32 q^{51} - 16 q^{53} - 16 q^{55} - 16 q^{57} - 8 q^{59} - 8 q^{61} - 56 q^{63} - 4 q^{65} + 24 q^{67} + 16 q^{69} + 32 q^{71} + 8 q^{73} - 4 q^{75} - 24 q^{77} + 24 q^{79} - 12 q^{81} + 112 q^{83} + 60 q^{87} + 12 q^{89} + 24 q^{91} - 16 q^{93} + 32 q^{97} - 88 q^{99} + O(q^{100}) \)

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.q.a 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.b 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
560.2.q.c 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
560.2.q.d 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
560.2.q.e 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.f 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
560.2.q.g 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
560.2.q.h 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
560.2.q.i 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.j 560.q 7.c $4$ $4.472$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.k 560.q 7.c $4$ $4.472$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.l 560.q 7.c $6$ $4.472$ 6.0.11337408.1 None \(0\) \(0\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)