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

• Label: 66.2.h
• Level: $66$
• Weight: $2$
• Character orbit: 66.h
• Rep. character: $\chi_{66}(17,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• 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.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
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	16	48
Cusp forms	32	16	16
Eisenstein series	32	0	32

Trace form

16 * q + 4 * q^3 - 4 * q^4 - 5 * q^6 - 16 * q^9 - 6 * q^12 - 12 * q^15 - 4 * q^16 - 5 * q^18 - 30 * q^19 + 12 * q^22 + 5 * q^24 - 12 * q^25 + 10 * q^27 + 10 * q^28 + 30 * q^30 + 26 * q^31 + 37 * q^33 + 20 * q^34 + 9 * q^36 + 12 * q^37 + 10 * q^39 + 10 * q^40 - 4 * q^42 - 16 * q^45 - 20 * q^46 + 4 * q^48 - 36 * q^49 - 15 * q^51 - 20 * q^52 - 28 * q^55 + 35 * q^57 - 46 * q^58 + 8 * q^60 - 20 * q^61 + 10 * q^63 - 4 * q^64 - 52 * q^66 - 4 * q^67 - 2 * q^69 - 34 * q^70 - 20 * q^72 + 10 * q^73 - 33 * q^75 - 16 * q^78 + 20 * q^79 - 12 * q^81 + 6 * q^82 + 60 * q^85 + 12 * q^88 + 10 * q^90 + 48 * q^91 - 26 * q^93 + 80 * q^94 + 18 * q^97 + 46 * 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.h.a	$66$	$2$	66.h	33.f	$10$	$8$	$2$	$0.527$	8.0.185640625.1	None		✓			66.2.h.a	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
66.2.h.b	$66$	$2$	66.h	33.f	$10$	$8$	$2$	$0.527$	8.0.185640625.1	None		✓			66.2.h.a	$2$	$0$	\(2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{6}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)

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

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