Space of modular forms of level 528, weight 5, and Character 528.j

• Label: 528.5.j
• Level: $528$
• Weight: $5$
• Character orbit: 528.j
• Rep. character: $\chi_{528}(241,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $480$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	528.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(480\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(528, [\chi])\).

	Total	New	Old
Modular forms	396	48	348
Cusp forms	372	48	324
Eisenstein series	24	0	24

Trace form

\( 48 q + 1296 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(528, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
528.5.j.a	$528$	$5$	528.j	11.b	$2$	$8$	$8$	$54.579$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-36\)	\(0\)	$2^{3}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(-5+\beta _{3}+\beta _{6})q^{5}+(-3\beta _{1}+\cdots)q^{7}+\cdots\)
528.5.j.b	$528$	$5$	528.j	11.b	$2$	$8$	$8$	$54.579$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-36\)	\(0\)	$2^{3}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-4+2\beta _{1}-\beta _{2})q^{5}-\beta _{5}q^{7}+\cdots\)
528.5.j.c	$528$	$5$	528.j	11.b	$2$	$8$	$8$	$54.579$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(72\)	\(0\)	$2^{9}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(9-2\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
528.5.j.d	$528$	$5$	528.j	11.b	$2$	$24$	$24$	$54.579$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(528, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)