Space of modular forms of level 280, weight 3, and Character 280.bi

• Label: 280.3.bi
• Level: $280$
• Weight: $3$
• Character orbit: 280.bi
• Rep. character: $\chi_{280}(179,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $184$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	280.bi (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(280, [\chi])\).

	Total	New	Old
Modular forms	200	200	0
Cusp forms	184	184	0
Eisenstein series	16	16	0

Trace form

\( 184 q - 2 q^{4} - 24 q^{6} + 248 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
280.3.bi.a	$280$	$3$	280.bi	280.ai	$6$	$4$	$2$	$7.629$	\(\Q(\sqrt{-3}, \sqrt{-10})\)	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(-4\)	\(0\)	\(10\)	\(-12\)	$2^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2+2\beta _{2})q^{2}-4\beta _{2}q^{4}+(5-5\beta _{2}+\cdots)q^{5}+\cdots\)
280.3.bi.b	$280$	$3$	280.bi	280.ai	$6$	$4$	$2$	$7.629$	\(\Q(\sqrt{-3}, \sqrt{-10})\)	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(4\)	\(0\)	\(-10\)	\(12\)	$2^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}-5\beta _{2}q^{5}+\cdots\)
280.3.bi.c	$280$	$3$	280.bi	280.ai	$6$	$176$	$88$	$7.629$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$