Space of modular forms of level 528, weight 6, and Character 528.o

• Label: 528.6.o
• Level: $528$
• Weight: $6$
• Character orbit: 528.o
• Rep. character: $\chi_{528}(175,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	528.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(528, [\chi])\).

	Total	New	Old
Modular forms	492	60	432
Cusp forms	468	60	408
Eisenstein series	24	0	24

Trace form

\( 60 q - 4860 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(528, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
528.6.o.a	$528$	$6$	528.o	44.c	$2$	$20$	$20$	$84.683$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	528.6.o.a	$4$	$0$	\(0\)	\(0\)	\(-88\)	\(0\)	$2^{43}\cdot 3^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(-4+\beta _{3})q^{5}-\beta _{7}q^{7}-3^{4}q^{9}+\cdots\)
528.6.o.b	$528$	$6$	528.o	44.c	$2$	$40$	$40$	$84.683$		None		✓	528.6.o.b	$4$	$0$	\(0\)	\(0\)	\(88\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(528, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)