Space of modular forms of level 280, weight 2, and Character 280.n

• Label: 280.2.n
• Level: $280$
• Weight: $2$
• Character orbit: 280.n
• Rep. character: $\chi_{280}(139,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(280, [\chi])\).

	Total	New	Old
Modular forms	52	52	0
Cusp forms	44	44	0
Eisenstein series	8	8	0

Trace form

\( 44 q - 4 q^{4} + 28 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(280, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
280.2.n.a	$280$	$2$	280.n	280.n	$2$	$4$	$4$	$2.236$	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}+2q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
280.2.n.b	$280$	$2$	280.n	280.n	$2$	$40$	$40$	$2.236$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$