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

• Label: 528.2.b
• Level: $528$
• Weight: $2$
• Character orbit: 528.b
• Rep. character: $\chi_{528}(65,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $6$
• Sturm bound: $192$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(192\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(17\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	108	26	82
Cusp forms	84	22	62
Eisenstein series	24	4	20

Trace form

\( 22 q + 2 q^{3} + 2 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
528.2.b.a	$528$	$2$	528.b	33.d	$2$	$2$	$2$	$4.216$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
528.2.b.b	$528$	$2$	528.b	33.d	$2$	$2$	$2$	$4.216$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta )q^{3}-\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.b.c	$528$	$2$	528.b	33.d	$2$	$2$	$2$	$4.216$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta )q^{3}-\beta q^{5}-3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
528.2.b.d	$528$	$2$	528.b	33.d	$2$	$4$	$4$	$4.216$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{2})q^{9}+\cdots\)
528.2.b.e	$528$	$2$	528.b	33.d	$2$	$6$	$6$	$4.216$	6.0.7388168.1	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
528.2.b.f	$528$	$2$	528.b	33.d	$2$	$6$	$6$	$4.216$	6.0.7388168.1	None		$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(528, [\chi]) \cong \)