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

• Label: 57.2.e
• Level: $57$
• Weight: $2$
• Character orbit: 57.e
• Rep. character: $\chi_{57}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $13$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

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

Trace form

8 * q - 2 * q^3 - 4 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^8 - 4 * q^9 + 4 * q^10 - 4 * q^11 + 12 * q^12 - 4 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 + 4 * q^17 - 4 * q^19 + 44 * q^20 + 2 * q^21 - 16 * q^22 - 10 * q^23 - 32 * q^26 + 4 * q^27 - 16 * q^28 + 4 * q^29 - 8 * q^30 + 24 * q^31 + 12 * q^32 - 2 * q^33 + 4 * q^34 - 18 * q^35 - 4 * q^36 + 42 * q^38 - 12 * q^39 + 24 * q^40 + 16 * q^41 + 4 * q^42 + 4 * q^43 - 14 * q^44 + 4 * q^45 + 32 * q^46 + 24 * q^47 - 6 * q^48 - 16 * q^49 - 56 * q^50 - 4 * q^51 + 2 * q^53 + 2 * q^54 - 12 * q^55 - 48 * q^56 - 6 * q^57 - 32 * q^58 - 10 * q^59 - 22 * q^60 + 26 * q^62 - 16 * q^64 + 12 * q^65 - 20 * q^66 - 20 * q^67 + 8 * q^68 + 36 * q^69 + 24 * q^70 + 12 * q^71 + 6 * q^72 - 8 * q^73 - 4 * q^74 + 20 * q^75 + 20 * q^76 + 20 * q^77 + 26 * q^78 - 12 * q^79 - 10 * q^80 - 4 * q^81 + 4 * q^82 - 8 * q^83 + 36 * q^84 + 18 * q^86 + 24 * q^87 + 24 * q^88 + 22 * q^89 + 4 * q^90 - 12 * q^91 - 2 * q^92 - 18 * q^93 + 2 * q^95 - 44 * q^96 + 20 * q^98 + 2 * 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.e.a	$57$	$2$	57.e	19.c	$3$	$2$	$1$	$0.455$	\(\Q(\sqrt{-3}) \)	None		✓			57.2.e.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
57.2.e.b	$57$	$2$	57.e	19.c	$3$	$6$	$3$	$0.455$	6.0.954288.1	None		✓	✓		57.2.e.b	$2$	$0$	\(1\)	\(-3\)	\(-2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)