Space of modular forms of level 880, weight 2, and Character 880.s

• Label: 880.2.s
• Level: $880$
• Weight: $2$
• Character orbit: 880.s
• Rep. character: $\chi_{880}(67,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $240$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(880, [\chi])\).

	Total	New	Old
Modular forms	296	240	56
Cusp forms	280	240	40
Eisenstein series	16	0	16

Trace form

240 * q + 8 * q^4 + 12 * q^8 - 240 * q^9 + 8 * q^16 - 28 * q^18 - 16 * q^19 - 12 * q^20 + 44 * q^28 - 8 * q^30 + 40 * q^32 + 40 * q^34 - 24 * q^35 - 32 * q^36 - 40 * q^38 - 40 * q^40 - 80 * q^42 - 32 * q^46 + 48 * q^47 - 112 * q^48 - 16 * q^51 + 76 * q^52 - 8 * q^58 + 16 * q^59 + 92 * q^60 - 32 * q^61 + 36 * q^62 + 32 * q^64 - 48 * q^67 - 52 * q^68 - 32 * q^69 + 128 * q^70 - 32 * q^71 - 20 * q^72 - 16 * q^73 - 32 * q^74 - 56 * q^75 + 152 * q^78 - 56 * q^80 + 240 * q^81 + 40 * q^82 + 72 * q^84 + 40 * q^86 - 112 * q^87 + 24 * q^88 + 104 * q^90 - 16 * q^91 + 16 * q^92 - 8 * q^94 + 72 * q^96 - 64 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(880, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
880.2.s.a	$880$	$2$	880.s	80.j	$4$	$4$	$2$	$7.027$	\(\Q(\zeta_{8})\)	None		✓			880.2.s.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
880.2.s.b	$880$	$2$	880.s	80.j	$4$	$236$	$118$	$7.027$		None		✓	✓		880.2.s.b	$2$	$0$	\(0\)	\(0\)	\(8\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)