Properties

Label 560.2.g
Level $560$
Weight $2$
Character orbit 560.g
Rep. character $\chi_{560}(449,\cdot)$
Character field $\Q$
Dimension $18$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

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

Total New Old
Modular forms 108 18 90
Cusp forms 84 18 66
Eisenstein series 24 0 24

Trace form

\( 18 q + 2 q^{5} - 18 q^{9} + O(q^{10}) \) \( 18 q + 2 q^{5} - 18 q^{9} - 12 q^{11} + 12 q^{15} + 8 q^{19} + 2 q^{25} - 4 q^{29} - 8 q^{31} - 28 q^{39} - 4 q^{41} - 10 q^{45} - 18 q^{49} - 20 q^{51} + 40 q^{55} + 36 q^{61} - 16 q^{65} - 16 q^{69} + 40 q^{71} - 12 q^{79} + 34 q^{81} + 20 q^{89} - 12 q^{91} + 32 q^{95} + 56 q^{99} + O(q^{100}) \)

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.g.a 560.g 5.b $2$ $4.472$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(-2-i)q^{5}-iq^{7}-6q^{9}+\cdots\)
560.2.g.b 560.g 5.b $2$ $4.472$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-2-i)q^{5}+iq^{7}+2q^{9}+\cdots\)
560.2.g.c 560.g 5.b $2$ $4.472$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+2i)q^{5}-iq^{7}+3q^{9}-4iq^{13}+\cdots\)
560.2.g.d 560.g 5.b $2$ $4.472$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}+q^{11}+\cdots\)
560.2.g.e 560.g 5.b $4$ $4.472$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots\)
560.2.g.f 560.g 5.b $6$ $4.472$ 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(\beta _{2}+\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)