Space of modular forms of level 528, weight 3, and Character 528.i

• Label: 528.3.i
• Level: $528$
• Weight: $3$
• Character orbit: 528.i
• Rep. character: $\chi_{528}(353,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	528.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(528, [\chi])\).

	Total	New	Old
Modular forms	204	40	164
Cusp forms	180	40	140
Eisenstein series	24	0	24

Trace form

\( 40 q - 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(528, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
528.3.i.a	$528$	$3$	528.i	3.b	$2$	$2$	$2$	$14.387$	\(\Q(\sqrt{-11}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}-2\beta q^{5}+8q^{7}+9q^{9}-\beta q^{11}+\cdots\)
528.3.i.b	$528$	$3$	528.i	3.b	$2$	$2$	$2$	$14.387$	\(\Q(\sqrt{-11}) \)	None		$2$	$0$	\(0\)	\(-5\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3+\beta )q^{3}+(1-2\beta )q^{5}-2q^{7}+\cdots\)
528.3.i.c	$528$	$3$	528.i	3.b	$2$	$4$	$4$	$14.387$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2})q^{3}+(\beta _{2}-2\beta _{3})q^{5}+\beta _{1}q^{7}+\cdots\)
528.3.i.d	$528$	$3$	528.i	3.b	$2$	$4$	$4$	$14.387$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(5\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2}-\beta _{3})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
528.3.i.e	$528$	$3$	528.i	3.b	$2$	$8$	$8$	$14.387$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-8\)	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(-\beta _{2}+\beta _{4}-2\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots\)
528.3.i.f	$528$	$3$	528.i	3.b	$2$	$20$	$20$	$14.387$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{26}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{6}q^{5}+(-1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(528, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)