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

• Label: 57.2.j
• Level: $57$
• Weight: $2$
• Character orbit: 57.j
• Rep. character: $\chi_{57}(2,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $30$
• Newform subspaces: $2$
• Sturm bound: $13$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.j (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
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	54	54	0
Cusp forms	30	30	0
Eisenstein series	24	24	0

Trace form

30 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 - 9 * q^12 - 9 * q^13 - 9 * q^15 + 30 * q^16 - 9 * q^19 + 3 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 18 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 15 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 - 15 * q^49 + 3 * q^51 - 60 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 48 * q^61 - 45 * q^63 + 42 * q^64 - 57 * q^66 + 33 * q^67 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 141 * q^73 + 12 * q^76 + 9 * q^78 + 42 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 114 * q^91 + 87 * q^93 - 18 * q^96 - 78 * q^97 + 12 * 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.j.a	$57$	$2$	57.j	57.j	$18$	$6$	$1$	$0.455$	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-3}) \)		✓			57.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{18}]$	\(q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+2\zeta_{18}q^{4}+\cdots\)
57.2.j.b	$57$	$2$	57.j	57.j	$18$	$24$	$4$	$0.455$		None		✓	✓		57.2.j.b	$4$	$0$	\(0\)	\(-9\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$