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

• Label: 56.2.m
• Level: $56$
• Weight: $2$
• Character orbit: 56.m
• Rep. character: $\chi_{56}(3,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	56.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	20	20	0
Cusp forms	12	12	0
Eisenstein series	8	8	0

Trace form

12 * q - 6 * q^3 - 12 * q^8 + 6 * q^10 - 6 * q^11 - 18 * q^12 + 6 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 24 * q^22 + 6 * q^24 + 6 * q^26 + 6 * q^28 - 12 * q^30 - 6 * q^33 + 18 * q^35 + 48 * q^36 - 24 * q^38 + 42 * q^40 - 30 * q^42 + 6 * q^44 - 18 * q^46 - 12 * q^49 - 48 * q^50 + 6 * q^51 - 24 * q^52 - 36 * q^54 - 36 * q^57 + 18 * q^58 + 42 * q^59 - 6 * q^60 - 72 * q^64 - 12 * q^65 + 12 * q^66 + 30 * q^67 - 36 * q^68 + 30 * q^70 + 18 * q^73 + 12 * q^74 + 24 * q^75 + 60 * q^78 + 36 * q^80 + 6 * q^81 + 54 * q^82 + 12 * q^84 + 6 * q^88 + 18 * q^89 - 72 * q^91 + 60 * q^92 - 12 * q^94 + 60 * q^96 - 6 * q^98 - 24 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
56.2.m.a	$56$	$2$	56.m	56.m	$6$	$12$	$6$	$0.447$	12.0.\(\cdots\).2	None		✓	✓	✓	56.2.m.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{8})q^{2}+(-1-\beta _{10})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)