Space of modular forms of level 132, weight 3, and Character 132.g

• Label: 132.3.g
• Level: $132$
• Weight: $3$
• Character orbit: 132.g
• Rep. character: $\chi_{132}(67,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$132 = 2^{2} \cdot 3 \cdot 11$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	132.g (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$4$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$72$
Trace bound:			$1$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(132, [\chi])$.

	Total	New	Old
Modular forms	52	20	32
Cusp forms	44	20	24
Eisenstein series	8	0	8

Trace form

20 * q - 4 * q^4 + 8 * q^5 - 12 * q^6 - 12 * q^8 - 60 * q^9 - 16 * q^10 - 8 * q^13 + 68 * q^14 + 52 * q^16 - 40 * q^17 + 44 * q^20 - 48 * q^21 - 36 * q^24 + 220 * q^25 - 36 * q^26 - 64 * q^28 + 40 * q^29 - 48 * q^30 - 100 * q^32 + 112 * q^34 + 12 * q^36 + 88 * q^37 - 272 * q^38 + 72 * q^40 - 200 * q^41 - 60 * q^42 + 88 * q^44 - 24 * q^45 + 304 * q^46 - 144 * q^48 - 188 * q^49 + 192 * q^50 + 248 * q^52 - 56 * q^53 + 36 * q^54 - 92 * q^56 + 144 * q^57 - 248 * q^58 - 84 * q^60 - 8 * q^61 - 88 * q^62 + 236 * q^64 + 176 * q^65 - 184 * q^68 - 192 * q^69 + 120 * q^70 + 36 * q^72 + 72 * q^73 - 136 * q^74 - 336 * q^76 + 108 * q^78 + 12 * q^80 + 180 * q^81 + 32 * q^82 + 240 * q^84 + 336 * q^85 - 296 * q^86 + 132 * q^88 - 536 * q^89 + 48 * q^90 - 100 * q^92 + 144 * q^93 + 128 * q^94 + 372 * q^96 + 24 * q^97 + 656 * q^98

Decomposition of $S_{3}^{\mathrm{new}}(132, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
132.3.g.a	$132$	$3$	132.g	4.b	$2$	$4$	$4$	$3.597$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			132.3.g.a	$2$	$0$	$-4$	$0$	$4$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{2}+\beta _{1}q^{3}+(-2-2\beta _{1}+\cdots)q^{4}+\cdots$
132.3.g.b	$132$	$3$	132.g	4.b	$2$	$16$	$16$	$3.597$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		132.3.g.b	$2$	$0$	$4$	$0$	$4$	$0$	$2^{21}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{7}q^{3}+(-\beta _{7}-\beta _{8})q^{4}+\cdots$

Decomposition of $S_{3}^{\mathrm{old}}(132, [\chi])$ into lower level spaces

$S_{3}^{\mathrm{old}}(132, [\chi]) \simeq$ $S_{3}^{\mathrm{new}}(12, [\chi])$$^{\oplus 2}$$\oplus$$S_{3}^{\mathrm{new}}(44, [\chi])$$^{\oplus 2}$