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

• 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: $9$

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 + 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

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.bw.a	$560$	$2$	560.bw	35.j	$6$	$4$	$2$	$4.472$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					140.2.q.a	$2$	$1$	\(0\)	\(-6\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)
560.2.bw.b	$560$	$2$	560.bw	35.j	$6$	$4$	$2$	$4.472$	\(\Q(\zeta_{12})\)	None					35.2.j.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\cdots\)
560.2.bw.c	$560$	$2$	560.bw	35.j	$6$	$4$	$2$	$4.472$	\(\Q(\zeta_{12})\)	None					70.2.i.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{12}q^{3}+(2\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
560.2.bw.d	$560$	$2$	560.bw	35.j	$6$	$4$	$2$	$4.472$	\(\Q(\zeta_{12})\)	None					70.2.i.b	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+(-2\zeta_{12}+\cdots)q^{7}+\cdots\)
560.2.bw.e	$560$	$2$	560.bw	35.j	$6$	$4$	$2$	$4.472$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					140.2.q.a	$2$	$0$	\(0\)	\(6\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots\)
560.2.bw.f	$560$	$2$	560.bw	35.j	$6$	$24$	$12$	$4.472$		None			✓		280.2.bg.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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