Properties

Label 560.4.g
Level $560$
Weight $4$
Character orbit 560.g
Rep. character $\chi_{560}(449,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $8$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 560.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(384\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(560, [\chi])\).

Total New Old
Modular forms 300 54 246
Cusp forms 276 54 222
Eisenstein series 24 0 24

Trace form

\( 54 q - 2 q^{5} - 486 q^{9} + 132 q^{11} + 12 q^{15} - 24 q^{19} + 22 q^{25} - 284 q^{29} - 264 q^{31} + 900 q^{39} - 236 q^{41} + 90 q^{45} - 2646 q^{49} + 636 q^{51} - 792 q^{55} - 132 q^{61} + 1104 q^{65}+ \cdots - 8104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
560.4.g.a 560.g 5.b $2$ $33.041$ \(\Q(\sqrt{-1}) \) None 140.4.e.a \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5 i q^{3}+(5 i-10)q^{5}-7 i q^{7}+\cdots\)
560.4.g.b 560.g 5.b $2$ $33.041$ \(\Q(\sqrt{-1}) \) None 140.4.e.b \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+7 i q^{3}+(-11 i-2)q^{5}+7 i q^{7}+\cdots\)
560.4.g.c 560.g 5.b $2$ $33.041$ \(\Q(\sqrt{-1}) \) None 70.4.c.a \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+7 i q^{3}+(-5 i+10)q^{5}+7 i q^{7}+\cdots\)
560.4.g.d 560.g 5.b $4$ $33.041$ \(\Q(i, \sqrt{6})\) None 140.4.e.c \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{5}-\beta _{1}q^{7}+\cdots\)
560.4.g.e 560.g 5.b $6$ $33.041$ 6.0.\(\cdots\).1 None 70.4.c.b \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2\beta _{3}-\beta _{5})q^{3}+(-3+\beta _{2}+3\beta _{3}+\cdots)q^{5}+\cdots\)
560.4.g.f 560.g 5.b $10$ $33.041$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 35.4.b.a \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(1+\beta _{6})q^{5}+\beta _{4}q^{7}+(-5+\cdots)q^{9}+\cdots\)
560.4.g.g 560.g 5.b $12$ $33.041$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 280.4.g.a \(0\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{9}q^{3}+(-1-\beta _{2}+\beta _{4})q^{5}-7\beta _{2}q^{7}+\cdots\)
560.4.g.h 560.g 5.b $16$ $33.041$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 280.4.g.b \(0\) \(0\) \(22\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(1+\beta _{3}-\beta _{4})q^{5}-7\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(560, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)