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

• Label: 880.2.bs
• Level: $880$
• Weight: $2$
• Character orbit: 880.bs
• Rep. character: $\chi_{880}(79,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $144$
• 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.bs (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 220 \)
Character field:			\(\Q(\zeta_{10})\)
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	624	144	480
Cusp forms	528	144	384
Eisenstein series	96	0	96

Trace form

\( 144 q - 36 q^{9} + 24 q^{25} - 60 q^{41} + 48 q^{45} + 120 q^{49} + 24 q^{69} - 36 q^{81} - 120 q^{85} - 24 q^{89}+O(q^{100}) \)

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.bs.a	$880$	$2$	880.bs	220.o	$10$	$48$	$12$	$7.027$		None		✓			880.2.bs.a	$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
880.2.bs.b	$880$	$2$	880.bs	220.o	$10$	$96$	$24$	$7.027$		None		✓	✓		880.2.bs.b	$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)