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

• Label: 68.2.b
• Level: $68$
• Weight: $2$
• Character orbit: 68.b
• Rep. character: $\chi_{68}(33,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	68.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	12	2	10
Cusp forms	6	2	4
Eisenstein series	6	0	6

Trace form

\( 2 q + 2 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
68.2.b.a	$68$	$2$	68.b	17.b	$2$	$2$	$2$	$0.543$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+2\beta q^{5}-3\beta q^{7}+q^{9}-\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(68, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(68, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)