Space of modular forms of level 5520, weight 2, and Character 5520.be

• Label: 5520.2.be
• Level: $5520$
• Weight: $2$
• Character orbit: 5520.be
• Rep. character: $\chi_{5520}(1471,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $2304$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5520.be (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(2304\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5520, [\chi])\).

	Total	New	Old
Modular forms	1176	96	1080
Cusp forms	1128	96	1032
Eisenstein series	48	0	48

Trace form

\( 96 q - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5520, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5520.2.be.a	$5520$	$2$	5520.be	92.b	$2$	$16$	$16$	$44.077$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{3}+\beta _{10}q^{5}+(-1-\beta _{4})q^{7}+\cdots\)
5520.2.be.b	$5520$	$2$	5520.be	92.b	$2$	$16$	$16$	$44.077$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{3}+\beta _{10}q^{5}+(1+\beta _{4})q^{7}-q^{9}+\cdots\)
5520.2.be.c	$5520$	$2$	5520.be	92.b	$2$	$32$	$32$	$44.077$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$
5520.2.be.d	$5520$	$2$	5520.be	92.b	$2$	$32$	$32$	$44.077$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2760, [\chi])\)\(^{\oplus 2}\)