Space of modular forms of level 528, weight 2, and Character 528.o

• Label: 528.2.o
• Level: $528$
• Weight: $2$
• Character orbit: 528.o
• Rep. character: $\chi_{528}(175,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(528, [\chi])\).

	Total	New	Old
Modular forms	108	12	96
Cusp forms	84	12	72
Eisenstein series	24	0	24

Trace form

\( 12 q - 12 q^{9} - 12 q^{25} - 12 q^{33} + 84 q^{49} - 48 q^{53} - 48 q^{77} + 12 q^{81} + 24 q^{89} - 48 q^{93} + 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(528, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
528.2.o.a	$528$	$2$	528.o	44.c	$2$	$4$	$4$	$4.216$	\(\Q(i, \sqrt{10})\)	None		✓			528.2.o.a	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-2q^{5}-\beta _{3}q^{7}-q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
528.2.o.b	$528$	$2$	528.o	44.c	$2$	$8$	$8$	$4.216$	8.0.454201344.7	None		✓	✓		528.2.o.b	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-\beta _{7}q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

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