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

• Label: 56.2.i
• Level: $56$
• Weight: $2$
• Character orbit: 56.i
• Rep. character: $\chi_{56}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	24	4	20
Cusp forms	8	4	4
Eisenstein series	16	0	16

Trace form

\( 4 q - 2 q^{3} + 2 q^{5} - 4 q^{9} + O(q^{10}) \)

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.i.a	$56$	$2$	56.i	7.c	$3$	$2$	$1$	$0.447$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-3\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
56.2.i.b	$56$	$2$	56.i	7.c	$3$	$2$	$1$	$0.447$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(56, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(56, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)