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

• Label: 280.2.h
• Level: $280$
• Weight: $2$
• Character orbit: 280.h
• Rep. character: $\chi_{280}(251,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(13\)

Dimensions

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

	Total	New	Old
Modular forms	52	32	20
Cusp forms	44	32	12
Eisenstein series	8	0	8

Trace form

32 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 32 * q^9 - 8 * q^11 + 6 * q^14 + 18 * q^16 - 30 * q^18 + 12 * q^22 + 32 * q^25 - 2 * q^28 - 38 * q^32 + 30 * q^36 + 64 * q^42 - 8 * q^43 - 40 * q^44 + 12 * q^46 - 16 * q^49 + 2 * q^50 - 80 * q^51 + 34 * q^56 - 32 * q^57 + 36 * q^58 + 28 * q^60 - 46 * q^64 + 40 * q^67 - 8 * q^70 - 26 * q^72 - 56 * q^74 - 12 * q^78 + 48 * q^81 - 32 * q^84 - 48 * q^86 - 88 * q^88 - 64 * q^91 - 60 * q^92 - 34 * q^98 + 40 * q^99

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.h.a	$280$	$2$	280.h	56.e	$2$	$16$	$16$	$2.236$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			280.2.h.a	$2$	$0$	\(1\)	\(0\)	\(-16\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+\beta _{4}q^{3}+\beta _{9}q^{4}-q^{5}+\beta _{6}q^{6}+\cdots\)
280.2.h.b	$280$	$2$	280.h	56.e	$2$	$16$	$16$	$2.236$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			280.2.h.a	$2$	$0$	\(1\)	\(0\)	\(16\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-\beta _{4}q^{3}+\beta _{9}q^{4}+q^{5}-\beta _{6}q^{6}+\cdots\)

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

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