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

• Label: 280.2.bj
• Level: $280$
• Weight: $2$
• Character orbit: 280.bj
• Rep. character: $\chi_{280}(131,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $6$
• Sturm bound: $96$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	104	64	40
Cusp forms	88	64	24
Eisenstein series	16	0	16

Trace form

\( 64 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 32 q^{9} + O(q^{10}) \)

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.bj.a	$280$	$2$	280.bj	56.m	$6$	$4$	$2$	$2.236$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(-4\)	\(-6\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2})q^{3}+\cdots\)
280.2.bj.b	$280$	$2$	280.bj	56.m	$6$	$4$	$2$	$2.236$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$1$	\(0\)	\(-6\)	\(-2\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(-2-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)
280.2.bj.c	$280$	$2$	280.bj	56.m	$6$	$4$	$2$	$2.236$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(-6\)	\(2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
280.2.bj.d	$280$	$2$	280.bj	56.m	$6$	$4$	$2$	$2.236$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(-6\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
280.2.bj.e	$280$	$2$	280.bj	56.m	$6$	$24$	$12$	$2.236$		None		$2$	$0$	\(-3\)	\(12\)	\(12\)	\(-10\)		$\mathrm{SU}(2)[C_{6}]$
280.2.bj.f	$280$	$2$	280.bj	56.m	$6$	$24$	$12$	$2.236$		None		$2$	$0$	\(3\)	\(12\)	\(-12\)	\(10\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)