Space of modular forms of level 59, weight 3, and Character 59.d

• Label: 59.3.d
• Level: $59$
• Weight: $3$
• Character orbit: 59.d
• Rep. character: $\chi_{59}(2,\cdot)$
• Character field: $\Q(\zeta_{58})$
• Dimension: $252$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	59.d (of order \(58\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 59 \)
Character field:			\(\Q(\zeta_{58})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(59, [\chi])\).

	Total	New	Old
Modular forms	308	308	0
Cusp forms	252	252	0
Eisenstein series	56	56	0

Trace form

\( 252 q - 29 q^{2} - 33 q^{3} - 11 q^{4} - 21 q^{5} - 29 q^{6} - 35 q^{7} - 29 q^{8} - 70 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(59, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
59.3.d.a	$59$	$3$	59.d	59.d	$58$	$252$	$9$	$1.608$		None		$2$	$0$	\(-29\)	\(-33\)	\(-21\)	\(-35\)		$\mathrm{SU}(2)[C_{58}]$