Space of modular forms of level 880, weight 4, and Character 880.f

• Label: 880.4.f
• Level: $880$
• Weight: $4$
• Character orbit: 880.f
• Rep. character: $\chi_{880}(351,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $576$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	880.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(576\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(880, [\chi])\).

	Total	New	Old
Modular forms	444	72	372
Cusp forms	420	72	348
Eisenstein series	24	0	24

Trace form

\( 72 q - 768 q^{9} + 1800 q^{25} + 456 q^{33} + 3216 q^{49} + 2352 q^{53} - 6240 q^{69} - 2520 q^{77} + 6312 q^{81} - 1032 q^{89} - 672 q^{93} - 1680 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(880, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
880.4.f.a	$880$	$4$	880.f	44.c	$2$	$12$	$12$	$51.922$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			880.4.f.a	$4$	$0$	\(0\)	\(0\)	\(-60\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}-5q^{5}-\beta _{7}q^{7}+(-13+\beta _{4}+\cdots)q^{9}+\cdots\)
880.4.f.b	$880$	$4$	880.f	44.c	$2$	$12$	$12$	$51.922$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			880.4.f.b	$4$	$0$	\(0\)	\(0\)	\(60\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+5q^{5}+\beta _{6}q^{7}+(-13-\beta _{1}+\cdots)q^{9}+\cdots\)
880.4.f.c	$880$	$4$	880.f	44.c	$2$	$24$	$24$	$51.922$		None		✓			880.4.f.c	$4$	$0$	\(0\)	\(0\)	\(-120\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
880.4.f.d	$880$	$4$	880.f	44.c	$2$	$24$	$24$	$51.922$		None		✓			880.4.f.d	$4$	$0$	\(0\)	\(0\)	\(120\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)