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

• Label: 57.2.i
• Level: $57$
• Weight: $2$
• Character orbit: 57.i
• Rep. character: $\chi_{57}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $13$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.i (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
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	18	36
Cusp forms	30	18	12
Eisenstein series	24	0	24

Trace form

18 * q - 6 * q^4 - 6 * q^6 - 6 * q^7 - 24 * q^10 - 6 * q^11 - 6 * q^12 - 9 * q^13 + 6 * q^14 + 12 * q^15 + 18 * q^16 + 9 * q^19 - 12 * q^20 + 3 * q^21 - 24 * q^22 + 24 * q^24 - 12 * q^25 + 12 * q^26 - 3 * q^27 + 30 * q^28 + 12 * q^29 - 24 * q^31 - 6 * q^32 - 6 * q^33 + 42 * q^34 + 24 * q^35 - 6 * q^36 + 24 * q^38 + 6 * q^40 - 12 * q^41 - 12 * q^42 + 33 * q^43 + 24 * q^44 - 6 * q^45 + 18 * q^46 - 42 * q^47 - 24 * q^48 + 3 * q^49 + 18 * q^50 - 12 * q^51 - 18 * q^52 - 54 * q^53 - 6 * q^54 - 18 * q^55 - 72 * q^56 - 12 * q^57 - 48 * q^58 - 30 * q^59 - 12 * q^60 - 48 * q^62 + 6 * q^63 - 18 * q^64 + 36 * q^65 + 48 * q^66 + 33 * q^67 - 18 * q^68 + 12 * q^70 - 12 * q^71 + 36 * q^72 - 51 * q^73 + 60 * q^74 + 42 * q^75 - 60 * q^76 + 96 * q^77 + 36 * q^79 + 66 * q^80 - 18 * q^82 + 18 * q^83 + 18 * q^85 + 48 * q^86 + 24 * q^87 + 48 * q^88 + 48 * q^89 - 6 * q^90 + 12 * q^91 + 72 * q^92 + 12 * q^94 - 66 * q^95 - 24 * q^96 - 6 * 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.i.a	$57$	$2$	57.i	19.e	$9$	$6$	$1$	$0.455$	\(\Q(\zeta_{18})\)	None		✓			57.2.i.a	$2$	$0$	\(3\)	\(0\)	\(-6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}-\zeta_{18}^{4}q^{3}+\cdots\)
57.2.i.b	$57$	$2$	57.i	19.e	$9$	$12$	$2$	$0.455$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		57.2.i.b	$2$	$0$	\(-3\)	\(0\)	\(6\)	\(-9\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{6}q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(57, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(57, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)