Space of modular forms of level 17, weight 2, and Character 17.d

• Label: 17.2.d
• Level: $17$
• Weight: $2$
• Character orbit: 17.d
• Rep. character: $\chi_{17}(2,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(17, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

Trace form

4 * q - 4 * q^2 - 4 * q^3 + 4 * q^6 - 4 * q^7 + 4 * q^8 + 8 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 4 * q^14 - 8 * q^15 - 12 * q^16 - 12 * q^18 + 8 * q^19 + 4 * q^20 + 12 * q^22 + 4 * q^23 + 12 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 + 4 * q^28 - 4 * q^29 - 12 * q^31 + 4 * q^32 - 20 * q^34 + 8 * q^35 - 8 * q^40 - 4 * q^41 - 8 * q^42 - 8 * q^43 - 20 * q^44 + 12 * q^45 + 20 * q^46 + 12 * q^48 + 8 * q^49 + 20 * q^50 + 28 * q^51 + 16 * q^52 - 4 * q^53 - 8 * q^54 - 20 * q^56 - 24 * q^57 - 8 * q^60 - 12 * q^62 - 12 * q^63 - 4 * q^65 + 8 * q^66 + 16 * q^67 + 12 * q^68 - 32 * q^69 - 8 * q^70 + 20 * q^71 - 28 * q^73 + 20 * q^74 - 12 * q^75 + 8 * q^76 + 8 * q^77 - 8 * q^78 - 4 * q^79 + 4 * q^82 + 16 * q^83 + 32 * q^84 + 4 * q^85 + 8 * q^86 + 16 * q^87 + 12 * q^88 + 4 * q^90 - 28 * q^92 + 24 * q^93 - 24 * q^94 - 8 * q^95 - 20 * q^96 + 24 * q^97 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(17, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
17.2.d.a	$17$	$2$	17.d	17.d	$8$	$4$	$1$	$0.136$	\(\Q(\zeta_{8})\)	None		✓	✓	✓	17.2.d.a	$2$	$0$	\(-4\)	\(-4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)