Space of modular forms of level 34, weight 2, and trivial character

• Label: 34.2.a
• Level: $34$
• Weight: $2$
• Character orbit: 34.a
• Rep. character: $\chi_{34}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 34 = 2 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	34.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(34))\).

	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.

\(2\)	\(17\)	Fricke	Dim
\(-\)	\(+\)	\(-\)	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(1\)

Trace form

q + q^2 - 2 * q^3 + q^4 - 2 * q^6 - 4 * q^7 + q^8 + q^9 + 6 * q^11 - 2 * q^12 + 2 * q^13 - 4 * q^14 + q^16 - q^17 + q^18 - 4 * q^19 + 8 * q^21 + 6 * q^22 - 2 * q^24 - 5 * q^25 + 2 * q^26 + 4 * q^27 - 4 * q^28 - 4 * q^31 + q^32 - 12 * q^33 - q^34 + q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 + 6 * q^41 + 8 * q^42 + 8 * q^43 + 6 * q^44 - 2 * q^48 + 9 * q^49 - 5 * q^50 + 2 * q^51 + 2 * q^52 - 6 * q^53 + 4 * q^54 - 4 * q^56 + 8 * q^57 - 4 * q^61 - 4 * q^62 - 4 * q^63 + q^64 - 12 * q^66 + 8 * q^67 - q^68 + q^72 + 2 * q^73 - 4 * q^74 + 10 * q^75 - 4 * q^76 - 24 * q^77 - 4 * q^78 + 8 * q^79 - 11 * q^81 + 6 * q^82 + 8 * q^84 + 8 * q^86 + 6 * q^88 - 6 * q^89 - 8 * q^91 + 8 * q^93 - 2 * q^96 + 14 * q^97 + 9 * q^98 + 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(34))\) 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	17
34.2.a.a	$34$	$2$	34.a	1.a	$1$	$1$	$1$	$0.271$	\(\Q\)	None	✓	✓	✓	✓	34.2.a.a	$1$	$0$	\(1\)	\(-2\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}-4q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(34))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(34)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)