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

• Label: 132.2.i
• Level: $132$
• Weight: $2$
• Character orbit: 132.i
• Rep. character: $\chi_{132}(25,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.i (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	120	8	112
Cusp forms	72	8	64
Eisenstein series	48	0	48

Trace form

8 * q - 4 * q^5 + 10 * q^7 - 2 * q^9 + 10 * q^11 + 6 * q^13 - 10 * q^15 - 10 * q^17 + 8 * q^19 - 16 * q^21 - 12 * q^23 - 8 * q^25 - 12 * q^29 + 8 * q^31 - 2 * q^33 - 20 * q^35 + 6 * q^37 + 8 * q^39 - 28 * q^41 - 8 * q^43 - 4 * q^45 + 18 * q^47 - 4 * q^49 + 12 * q^51 + 18 * q^53 - 20 * q^55 + 24 * q^57 + 30 * q^59 + 14 * q^61 + 10 * q^63 + 52 * q^65 - 36 * q^67 + 2 * q^69 + 32 * q^71 - 12 * q^73 + 14 * q^77 + 10 * q^79 - 2 * q^81 - 2 * q^83 + 30 * q^85 + 8 * q^87 + 28 * q^89 - 6 * q^91 - 12 * q^93 - 14 * q^95 - 46 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
132.2.i.a	$132$	$2$	132.i	11.c	$5$	$4$	$1$	$1.054$	\(\Q(\zeta_{10})\)	None		✓			132.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}^{3})q^{5}+(2\zeta_{10}+\cdots)q^{7}+\cdots\)
132.2.i.b	$132$	$2$	132.i	11.c	$5$	$4$	$1$	$1.054$	\(\Q(\zeta_{10})\)	None		✓			132.2.i.b	$2$	$0$	\(0\)	\(1\)	\(-7\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{3}q^{3}+(-1-2\zeta_{10}+2\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(132, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)