Space of modular forms of level 132, weight 2, and Character 132.b

• Label: 132.2.b
• Level: $132$
• Weight: $2$
• Character orbit: 132.b
• Rep. character: $\chi_{132}(65,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(132, [\chi])\).

	Total	New	Old
Modular forms	30	4	26
Cusp forms	18	4	14
Eisenstein series	12	0	12

Trace form

\( 4 q - q^{3} + 5 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(132, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
132.2.b.a	$132$	$2$	132.b	33.d	$2$	$4$	$4$	$1.054$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(132, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(132, [\chi]) \cong \)