Space of modular forms of level 280, weight 6, and Character 280.q

• Label: 280.6.q
• Level: $280$
• Weight: $6$
• Character orbit: 280.q
• Rep. character: $\chi_{280}(81,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	280.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(280, [\chi])\).

	Total	New	Old
Modular forms	496	80	416
Cusp forms	464	80	384
Eisenstein series	32	0	32

Trace form

\( 80 q + 36 q^{3} - 50 q^{5} - 124 q^{7} - 3430 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(280, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
280.6.q.a	$280$	$6$	280.q	7.c	$3$	$18$	$9$	$44.907$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(21\)	\(225\)	\(-15\)	$2^{28}\cdot 3\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+\beta _{1}-2\beta _{3})q^{3}+5^{2}\beta _{3}q^{5}+(5+\cdots)q^{7}+\cdots\)
280.6.q.b	$280$	$6$	280.q	7.c	$3$	$20$	$10$	$44.907$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(-3\)	\(250\)	\(-105\)	$2^{34}\cdot 3^{2}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}-5^{2}\beta _{4}q^{5}+(-8-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
280.6.q.c	$280$	$6$	280.q	7.c	$3$	$20$	$10$	$44.907$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(16\)	\(-250\)	\(136\)	$2^{32}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2\beta _{3}+\beta _{4})q^{3}+(-5^{2}-5^{2}\beta _{3}+\cdots)q^{5}+\cdots\)
280.6.q.d	$280$	$6$	280.q	7.c	$3$	$22$	$11$	$44.907$		None		$2$	$0$	\(0\)	\(2\)	\(-275\)	\(-140\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{6}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)