Space of modular forms of level 56, weight 2, and Character 56.e

• Label: 56.2.e
• Level: $56$
• Weight: $2$
• Character orbit: 56.e
• Rep. character: $\chi_{56}(27,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	56.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(56, [\chi])\).

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

Trace form

\( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(56, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
56.2.e.a	$56$	$2$	56.e	56.e	$2$	$2$	$2$	$0.447$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+(-2+\beta )q^{4}+(1-2\beta )q^{7}+\cdots\)
56.2.e.b	$56$	$2$	56.e	56.e	$2$	$4$	$4$	$0.447$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+\cdots\)