Space of modular forms of level 34, weight 2, and Character 34.b

• Label: 34.2.b
• Level: $34$
• Weight: $2$
• Character orbit: 34.b
• Rep. character: $\chi_{34}(33,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 34 = 2 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	34.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(34, [\chi])\).

	Total	New	Old
Modular forms	6	2	4
Cusp forms	2	2	0
Eisenstein series	4	0	4

Trace form

2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 10 * q^9 + 4 * q^13 + 16 * q^15 + 2 * q^16 - 6 * q^17 + 10 * q^18 - 8 * q^19 - 6 * q^25 - 4 * q^26 - 16 * q^30 - 2 * q^32 + 16 * q^33 + 6 * q^34 - 10 * q^36 + 8 * q^38 - 8 * q^43 + 14 * q^49 + 6 * q^50 - 16 * q^51 + 4 * q^52 + 12 * q^53 - 16 * q^55 + 24 * q^59 + 16 * q^60 + 2 * q^64 - 16 * q^66 - 8 * q^67 - 6 * q^68 - 32 * q^69 + 10 * q^72 - 8 * q^76 + 2 * q^81 - 24 * q^83 + 16 * q^85 + 8 * q^86 + 16 * q^87 + 12 * q^89 - 14 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(34, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
34.2.b.a	$34$	$2$	34.b	17.b	$2$	$2$	$2$	$0.271$	\(\Q(\sqrt{-2}) \)	None		✓	✓	✓	34.2.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)