Space of modular forms of level 57, weight 3, and Character 57.c

• Label: 57.3.c
• Level: $57$
• Weight: $3$
• Character orbit: 57.c
• Rep. character: $\chi_{57}(37,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	57.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(20\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(57, [\chi])\).

	Total	New	Old
Modular forms	16	6	10
Cusp forms	12	6	6
Eisenstein series	4	0	4

Trace form

\( 6 q - 4 q^{4} - 2 q^{5} - 12 q^{6} + 14 q^{7} - 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(57, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
57.3.c.a	$57$	$3$	57.c	19.b	$2$	$2$	$2$	$1.553$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(-20\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+q^{4}+4q^{5}-3q^{6}+\cdots\)
57.3.c.b	$57$	$3$	57.c	19.b	$2$	$4$	$4$	$1.553$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(34\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{3})q^{2}-\beta _{1}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(57, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(57, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)