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

• Label: 34.2.d
• Level: $34$
• Weight: $2$
• Character orbit: 34.d
• Rep. character: $\chi_{34}(9,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 34 = 2 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	34.d (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
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	28	4	24
Cusp forms	12	4	8
Eisenstein series	16	0	16

Trace form

\( 4 q - 8 q^{5} - 4 q^{9} + O(q^{10}) \)

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.d.a	$34$	$2$	34.d	17.d	$8$	$4$	$1$	$0.271$	\(\Q(\zeta_{8})\)	None		✓	✓	✓	34.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(34, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(34, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)