Space of modular forms of level 59, weight 2, and Character 59.c

• Label: 59.2.c
• Level: $59$
• Weight: $2$
• Character orbit: 59.c
• Rep. character: $\chi_{59}(3,\cdot)$
• Character field: $\Q(\zeta_{29})$
• Dimension: $112$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	59.c (of order \(29\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 59 \)
Character field:			\(\Q(\zeta_{29})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(59, [\chi])\).

	Total	New	Old
Modular forms	168	168	0
Cusp forms	112	112	0
Eisenstein series	56	56	0

Trace form

\( 112 q - 26 q^{2} - 23 q^{3} - 30 q^{4} - 25 q^{5} - 13 q^{6} - 23 q^{7} - 8 q^{8} - 21 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(59, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
59.2.c.a	$59$	$2$	59.c	59.c	$29$	$112$	$4$	$0.471$		None		$2$	$0$	\(-26\)	\(-23\)	\(-25\)	\(-23\)		$\mathrm{SU}(2)[C_{29}]$