Space of modular forms of level 560, weight 2, and Character 560.g

• 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: $9$

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 - 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

Decomposition of \(S_{2}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.2.g.a	$560$	$2$	560.g	5.b	$2$	$2$	$2$	$4.472$	\(\Q(\sqrt{-1}) \)	None					140.2.e.a	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+(-i-2)q^{5}-i q^{7}-6 q^{9}+\cdots\)
560.2.g.b	$560$	$2$	560.g	5.b	$2$	$2$	$2$	$4.472$	\(\Q(\sqrt{-1}) \)	None					35.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-i-2)q^{5}+i q^{7}+2 q^{9}+\cdots\)
560.2.g.c	$560$	$2$	560.g	5.b	$2$	$2$	$2$	$4.472$	\(\Q(\sqrt{-1}) \)	None					140.2.e.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2 i+1)q^{5}-i q^{7}+3 q^{9}-4 i q^{13}+\cdots\)
560.2.g.d	$560$	$2$	560.g	5.b	$2$	$2$	$2$	$4.472$	\(\Q(\sqrt{-1}) \)	None					280.2.g.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i+2)q^{5}+i q^{7}+2 q^{9}+\cdots\)
560.2.g.e	$560$	$2$	560.g	5.b	$2$	$4$	$4$	$4.472$	\(\Q(i, \sqrt{6})\)	None					70.2.c.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots\)
560.2.g.f	$560$	$2$	560.g	5.b	$2$	$6$	$6$	$4.472$	6.0.5161984.1	None			✓		280.2.g.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(\beta _{2}+\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)

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

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