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

• Label: 280.2.bl
• Level: $280$
• Weight: $2$
• Character orbit: 280.bl
• Rep. character: $\chi_{280}(221,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• 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.bl (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
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	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 - 10 * q^12 + 18 * q^14 - 14 * q^16 - 8 * q^20 - 40 * q^22 - 8 * q^23 - 32 * q^24 + 32 * q^25 - 2 * q^26 - 22 * q^28 + 2 * q^32 - 40 * q^34 + 20 * q^36 - 40 * q^38 - 62 * q^42 + 26 * q^44 + 22 * q^46 - 40 * q^47 + 124 * q^48 + 16 * q^49 + 4 * q^50 + 12 * q^52 - 40 * q^54 - 32 * q^55 + 24 * q^56 - 32 * q^57 + 6 * q^58 + 14 * q^60 - 16 * q^62 - 80 * q^63 + 4 * q^64 + 60 * q^66 + 28 * q^68 + 20 * q^70 - 48 * q^71 - 60 * q^72 + 16 * q^73 - 42 * q^74 - 20 * q^76 - 40 * q^78 + 40 * q^79 - 40 * q^81 - 34 * q^82 - 8 * q^84 - 56 * q^86 + 48 * q^87 - 4 * q^88 + 8 * q^89 - 36 * q^90 + 84 * q^92 - 66 * q^94 - 16 * q^96 - 64 * q^97 - 58 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
280.2.bl.a	$280$	$2$	280.bl	56.p	$6$	$4$	$2$	$2.236$	\(\Q(\zeta_{12})\)	None		✓			280.2.bl.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
280.2.bl.b	$280$	$2$	280.bl	56.p	$6$	$60$	$30$	$2.236$		None		✓	✓		280.2.bl.b	$4$	$0$	\(4\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{6}]$

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

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