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

• Label: 880.2.w
• Level: $880$
• Weight: $2$
• Character orbit: 880.w
• Rep. character: $\chi_{880}(221,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $160$
• 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.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
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	160	136
Cusp forms	280	160	120
Eisenstein series	16	0	16

Trace form

160 * q + 24 * q^6 - 8 * q^10 + 24 * q^12 - 8 * q^14 + 16 * q^15 + 8 * q^16 + 40 * q^18 + 16 * q^19 - 8 * q^20 - 48 * q^24 - 48 * q^27 - 40 * q^28 + 40 * q^32 + 8 * q^34 + 8 * q^36 - 40 * q^38 - 80 * q^42 + 8 * q^44 + 72 * q^46 + 80 * q^47 + 40 * q^48 - 160 * q^49 + 64 * q^51 - 32 * q^54 + 16 * q^56 - 16 * q^58 + 32 * q^59 - 32 * q^61 - 72 * q^62 + 72 * q^64 + 40 * q^66 - 8 * q^68 - 32 * q^69 + 8 * q^70 + 40 * q^72 + 112 * q^74 - 64 * q^76 - 24 * q^78 - 32 * q^79 - 160 * q^81 + 72 * q^82 - 80 * q^83 + 32 * q^85 - 24 * q^86 - 72 * q^90 + 16 * q^91 + 48 * q^92 + 96 * q^93 + 24 * q^94 - 64 * q^96 - 120 * 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.w.a	$880$	$2$	880.w	16.e	$4$	$72$	$36$	$7.027$		None		✓			880.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
880.2.w.b	$880$	$2$	880.w	16.e	$4$	$88$	$44$	$7.027$		None		✓	✓		880.2.w.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)