Space of modular forms of level 33, weight 2, and trivial character

• Label: 33.2.a
• Level: $33$
• Weight: $2$
• Character orbit: 33.a
• Rep. character: $\chi_{33}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	33.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(33))\).

	Total	New	Old
Modular forms	6	1	5
Cusp forms	3	1	2
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(11\)	Fricke	Dim
\(+\)	\(-\)	\(-\)	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(1\)

Trace form

q + q^2 - q^3 - q^4 - 2 * q^5 - q^6 + 4 * q^7 - 3 * q^8 + q^9 - 2 * q^10 + q^11 + q^12 - 2 * q^13 + 4 * q^14 + 2 * q^15 - q^16 - 2 * q^17 + q^18 + 2 * q^20 - 4 * q^21 + q^22 + 8 * q^23 + 3 * q^24 - q^25 - 2 * q^26 - q^27 - 4 * q^28 - 6 * q^29 + 2 * q^30 - 8 * q^31 + 5 * q^32 - q^33 - 2 * q^34 - 8 * q^35 - q^36 + 6 * q^37 + 2 * q^39 + 6 * q^40 - 2 * q^41 - 4 * q^42 - q^44 - 2 * q^45 + 8 * q^46 + 8 * q^47 + q^48 + 9 * q^49 - q^50 + 2 * q^51 + 2 * q^52 + 6 * q^53 - q^54 - 2 * q^55 - 12 * q^56 - 6 * q^58 - 4 * q^59 - 2 * q^60 + 6 * q^61 - 8 * q^62 + 4 * q^63 + 7 * q^64 + 4 * q^65 - q^66 - 4 * q^67 + 2 * q^68 - 8 * q^69 - 8 * q^70 - 3 * q^72 - 14 * q^73 + 6 * q^74 + q^75 + 4 * q^77 + 2 * q^78 - 4 * q^79 + 2 * q^80 + q^81 - 2 * q^82 + 12 * q^83 + 4 * q^84 + 4 * q^85 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 2 * q^90 - 8 * q^91 - 8 * q^92 + 8 * q^93 + 8 * q^94 - 5 * q^96 + 2 * q^97 + 9 * q^98 + q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(33))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	11
33.2.a.a	$33$	$2$	33.a	1.a	$1$	$1$	$1$	$0.264$	\(\Q\)	None	✓	✓	✓	✓	33.2.a.a	$1$	$0$	\(1\)	\(-1\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(33))\) into lower level spaces

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