Space of modular forms of level 560, weight 3, and Character 560.bt

• Label: 560.3.bt
• Level: $560$
• Weight: $3$
• Character orbit: 560.bt
• Rep. character: $\chi_{560}(79,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.bt (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(560, [\chi])\).

	Total	New	Old
Modular forms	408	96	312
Cusp forms	360	96	264
Eisenstein series	48	0	48

Trace form

\( 96 q - 144 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.3.bt.a	$560$	$3$	560.bt	140.p	$6$	$8$	$4$	$15.259$	8.0.12960000.1	\(\Q(\sqrt{-5}) \)		✓	560.3.bt.a	$8$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$2^{12}\cdot 7$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{5}q^{3}-5\beta _{2}q^{5}+(\beta _{5}-\beta _{7})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
560.3.bt.b	$560$	$3$	560.bt	140.p	$6$	$24$	$12$	$15.259$		None		✓	560.3.bt.b	$8$	$0$	\(0\)	\(0\)	\(22\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
560.3.bt.c	$560$	$3$	560.bt	140.p	$6$	$32$	$16$	$15.259$		None		✓	560.3.bt.c	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
560.3.bt.d	$560$	$3$	560.bt	140.p	$6$	$32$	$16$	$15.259$		None		✓	560.3.bt.c	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

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