Space of modular forms of level 66, weight 2, and trivial character

• Label: 66.2.a
• Level: $66$
• Weight: $2$
• Character orbit: 66.a
• Rep. character: $\chi_{66}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $24$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(24\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(66))\).

	Total	New	Old
Modular forms	16	3	13
Cusp forms	9	3	6
Eisenstein series	7	0	7

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
\(+\)	\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(1\)
Plus space			\(+\)	\(0\)
Minus space			\(-\)	\(3\)

Trace form

3 * q + q^2 + q^3 + 3 * q^4 - 2 * q^5 - q^6 - 4 * q^7 + q^8 + 3 * q^9 - 2 * q^10 - q^11 + q^12 - 6 * q^13 - 8 * q^14 - 6 * q^15 + 3 * q^16 - 6 * q^17 + q^18 - 2 * q^20 + 4 * q^21 + q^22 + 4 * q^23 - q^24 + 5 * q^25 + 2 * q^26 + q^27 - 4 * q^28 + 22 * q^29 - 6 * q^30 + q^32 + q^33 + 6 * q^34 + 3 * q^36 - 6 * q^37 + 8 * q^38 + 6 * q^39 - 2 * q^40 + 2 * q^41 + 16 * q^43 - q^44 - 2 * q^45 - 8 * q^46 - 20 * q^47 + q^48 + 3 * q^49 + 15 * q^50 - 10 * q^51 - 6 * q^52 + 6 * q^53 - q^54 - 6 * q^55 - 8 * q^56 - 8 * q^57 + 10 * q^58 + 12 * q^59 - 6 * q^60 - 14 * q^61 - 16 * q^62 - 4 * q^63 + 3 * q^64 - 28 * q^65 + 3 * q^66 - 12 * q^67 - 6 * q^68 - 4 * q^69 - 4 * q^71 + q^72 - 10 * q^73 + 14 * q^74 + 7 * q^75 + 14 * q^78 + 20 * q^79 - 2 * q^80 + 3 * q^81 - 10 * q^82 - 4 * q^83 + 4 * q^84 + 12 * q^85 + 10 * q^87 + q^88 + 14 * q^89 - 2 * q^90 + 8 * q^91 + 4 * q^92 - 8 * q^94 + 8 * q^95 - q^96 - 2 * q^97 + 9 * q^98 - q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(66))\) 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
66.2.a.a	$66$	$2$	66.a	1.a	$1$	$1$	$1$	$0.527$	\(\Q\)	None	✓	✓	✓	✓	66.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
66.2.a.b	$66$	$2$	66.a	1.a	$1$	$1$	$1$	$0.527$	\(\Q\)	None	✓	✓	✓	✓	66.2.a.b	$1$	$0$	\(1\)	\(-1\)	\(2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots\)
66.2.a.c	$66$	$2$	66.a	1.a	$1$	$1$	$1$	$0.527$	\(\Q\)	None	✓	✓	✓	✓	66.2.a.c	$1$	$0$	\(1\)	\(1\)	\(-4\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(66))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(66)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)