Space of modular forms of level 66, weight 2, and Character 66.e

• Label: 66.2.e
• Level: $66$
• Weight: $2$
• Character orbit: 66.e
• Rep. character: $\chi_{66}(25,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$66 = 2 \cdot 3 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	66.e (of order $5$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$11$
Character field:			$\Q(\zeta_{5})$
Newform subspaces:			$2$
Sturm bound:			$24$
Trace bound:			$2$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(66, [\chi])$.

	Total	New	Old
Modular forms	64	8	56
Cusp forms	32	8	24
Eisenstein series	32	0	32

Trace form

8 * q - 2 * q^4 + 8 * q^5 + 2 * q^6 - 8 * q^7 - 2 * q^9 - 12 * q^10 - 8 * q^11 - 4 * q^14 + 2 * q^15 - 2 * q^16 - 16 * q^17 + 20 * q^19 + 8 * q^20 - 16 * q^21 + 10 * q^22 + 2 * q^24 - 14 * q^25 + 12 * q^26 + 2 * q^28 - 12 * q^29 + 12 * q^30 + 2 * q^31 + 10 * q^33 - 8 * q^34 + 28 * q^35 - 2 * q^36 + 24 * q^37 + 12 * q^38 + 8 * q^39 - 2 * q^40 + 20 * q^41 - 2 * q^42 - 32 * q^43 - 8 * q^44 + 8 * q^45 + 12 * q^46 - 12 * q^47 + 14 * q^49 - 24 * q^50 - 12 * q^51 - 12 * q^53 - 8 * q^54 - 8 * q^55 + 16 * q^56 - 12 * q^57 + 10 * q^58 - 12 * q^59 - 8 * q^60 - 4 * q^61 - 12 * q^62 - 8 * q^63 - 2 * q^64 - 8 * q^65 - 12 * q^66 - 16 * q^68 + 8 * q^69 - 22 * q^70 - 4 * q^71 - 6 * q^73 - 16 * q^74 + 24 * q^75 + 8 * q^77 - 20 * q^79 - 12 * q^80 - 2 * q^81 + 12 * q^82 + 28 * q^83 + 4 * q^84 - 24 * q^85 - 16 * q^86 + 20 * q^87 - 10 * q^88 + 16 * q^89 + 8 * q^90 + 24 * q^91 + 20 * q^92 + 12 * q^93 + 16 * q^94 + 52 * q^95 + 2 * q^96 + 20 * q^97 + 48 * q^98 + 12 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(66, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
66.2.e.a	$66$	$2$	66.e	11.c	$5$	$4$	$1$	$0.527$	$\Q(\zeta_{10})$	None		✓			66.2.e.a	$2$	$0$	$-1$	$1$	$8$	$-6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(2+\cdots)q^{5}+\cdots$
66.2.e.b	$66$	$2$	66.e	11.c	$5$	$4$	$1$	$0.527$	$\Q(\zeta_{10})$	None		✓			66.2.e.b	$2$	$0$	$1$	$-1$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(-2+\cdots)q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(66, [\chi])$ into lower level spaces

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