Space of modular forms of level 132, weight 4, and trivial character

• Label: 132.4.a
• Level: $132$
• Weight: $4$
• Character orbit: 132.a
• Rep. character: $\chi_{132}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	132.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(132))\).

	Total	New	Old
Modular forms	78	4	74
Cusp forms	66	4	62
Eisenstein series	12	0	12

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(11\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(-\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(1\)
Plus space			\(+\)	\(3\)
Minus space			\(-\)	\(1\)

Trace form

\( 4 q - 6 q^{3} + 20 q^{5} + 4 q^{7} + 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(132))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	11
132.4.a.a	$132$	$4$	132.a	1.a	$1$	$1$	$1$	$7.788$	\(\Q\)	None	✓	✓			132.4.a.a	$1$	$0$	\(0\)	\(-3\)	\(-12\)	\(14\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-12q^{5}+14q^{7}+9q^{9}+11q^{11}+\cdots\)
132.4.a.b	$132$	$4$	132.a	1.a	$1$	$1$	$1$	$7.788$	\(\Q\)	None	✓	✓	✓	✓	132.4.a.b	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{7}+9q^{9}-11q^{11}-88q^{13}+\cdots\)
132.4.a.c	$132$	$4$	132.a	1.a	$1$	$1$	$1$	$7.788$	\(\Q\)	None	✓	✓			132.4.a.c	$1$	$0$	\(0\)	\(-3\)	\(22\)	\(-20\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+22q^{5}-20q^{7}+9q^{9}+11q^{11}+\cdots\)
132.4.a.d	$132$	$4$	132.a	1.a	$1$	$1$	$1$	$7.788$	\(\Q\)	None	✓	✓	✓	✓	132.4.a.d	$1$	$0$	\(0\)	\(3\)	\(10\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+10q^{5}+8q^{7}+9q^{9}-11q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(132))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(132)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)