Space of modular forms of level 68, weight 2, and Character 68.i

• Label: 68.2.i
• Level: $68$
• Weight: $2$
• Character orbit: 68.i
• Rep. character: $\chi_{68}(3,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	68.i (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 68 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(68, [\chi])\).

	Total	New	Old
Modular forms	88	88	0
Cusp forms	56	56	0
Eisenstein series	32	32	0

Trace form

56 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 - 16 * q^25 + 24 * q^26 + 40 * q^28 - 16 * q^29 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 16 * q^41 + 40 * q^42 + 24 * q^44 - 16 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 - 8 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 88 * q^65 - 96 * q^66 - 96 * q^68 + 32 * q^69 - 80 * q^70 - 112 * q^72 + 88 * q^73 - 56 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 48 * q^82 - 8 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 72 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 128 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(68, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
68.2.i.a	$68$	$2$	68.i	68.i	$16$	$8$	$1$	$0.543$	\(\Q(\zeta_{16})\)	\(\Q(\sqrt{-1}) \)		✓			68.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{16}]$	\(q+(-\zeta_{16}+\zeta_{16}^{5})q^{2}-2\zeta_{16}^{6}q^{4}+\cdots\)
68.2.i.b	$68$	$2$	68.i	68.i	$16$	$48$	$6$	$0.543$		None		✓	✓		68.2.i.b	$4$	$0$	\(-8\)	\(0\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$