Space of modular forms of level 57, weight 2, and Character 57.f

• Label: 57.2.f
• Level: $57$
• Weight: $2$
• Character orbit: 57.f
• Rep. character: $\chi_{57}(8,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $13$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.f (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(13\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(57, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	8	8	0
Eisenstein series	8	8	0

Trace form

8 * q + 4 * q^6 - 16 * q^7 - 4 * q^9 - 12 * q^10 + 12 * q^13 + 4 * q^16 - 12 * q^21 + 12 * q^22 + 4 * q^24 - 12 * q^25 + 12 * q^28 - 8 * q^30 + 24 * q^33 + 24 * q^34 + 16 * q^39 - 12 * q^40 - 20 * q^42 - 16 * q^43 + 32 * q^45 + 24 * q^48 - 48 * q^51 - 24 * q^52 - 4 * q^54 + 16 * q^55 - 28 * q^57 - 64 * q^58 - 24 * q^60 + 28 * q^61 + 8 * q^63 - 32 * q^64 - 4 * q^66 + 36 * q^70 - 24 * q^72 + 12 * q^73 + 60 * q^76 + 36 * q^78 + 24 * q^79 + 28 * q^81 + 16 * q^82 + 32 * q^87 + 12 * q^90 - 48 * q^91 - 4 * q^93 + 72 * q^96 + 24 * q^97 - 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(57, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
57.2.f.a	$57$	$2$	57.f	57.f	$6$	$8$	$4$	$0.455$	\(\Q(\zeta_{24})\)	None		✓	✓	✓	57.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)