Space of modular forms of level 248, weight 1, and Character 248.g

• Label: 248.1.g
• Level: $248$
• Weight: $1$
• Character orbit: 248.g
• Rep. character: $\chi_{248}(61,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 248 = 2^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	248.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 248 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(248, [\chi])\).

	Total	New	Old
Modular forms	7	7	0
Cusp forms	5	5	0
Eisenstein series	2	2	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	5	0	0	0

Trace form

\( 5 q - 2 q^{2} + 2 q^{4} + q^{8} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(248, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
248.1.g.a	$248$	$1$	248.g	248.g	$2$	$1$	$1$	$0.124$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-62}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+q^{2}+q^{4}-2q^{7}+q^{8}-q^{9}-2q^{14}+\cdots\)
248.1.g.b	$248$	$1$	248.g	248.g	$2$	$2$	$2$	$0.124$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-62}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots\)
248.1.g.c	$248$	$1$	248.g	248.g	$2$	$2$	$2$	$0.124$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-31}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots\)