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 - 8 * q^10 + 4 * q^11 + 4 * q^12 + 8 * q^14 + 8 * q^15 - 4 * q^16 + 4 * q^18 + 8 * q^19 + 8 * q^22 - 16 * q^23 + 4 * q^24 + 16 * q^25 - 8 * q^26 - 12 * q^27 - 8 * q^28 - 16 * q^33 - 16 * q^34 - 4 * q^36 - 8 * q^37 + 16 * q^41 + 8 * q^42 + 12 * q^43 + 8 * q^44 + 8 * q^45 - 16 * q^49 + 12 * q^50 + 16 * q^51 + 8 * q^52 + 8 * q^53 + 4 * q^54 + 8 * q^57 - 4 * q^59 - 8 * q^60 + 16 * q^61 - 8 * q^63 - 16 * q^65 - 12 * q^66 - 24 * q^67 - 16 * q^70 - 8 * q^71 + 8 * q^74 - 28 * q^75 - 8 * q^76 + 8 * q^77 - 8 * q^79 + 8 * q^80 + 20 * q^82 + 12 * q^83 - 8 * q^85 - 24 * q^86 + 8 * q^87 + 4 * q^88 + 32 * q^91 - 8 * q^93 + 16 * q^94 - 12 * q^97

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

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