Space of modular forms of level 59, weight 4, and Character 59.c

• Label: 59.4.c
• Level: $59$
• Weight: $4$
• Character orbit: 59.c
• Rep. character: $\chi_{59}(3,\cdot)$
• Character field: $\Q(\zeta_{29})$
• Dimension: $392$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(59, [\chi])\).

	Total	New	Old
Modular forms	448	448	0
Cusp forms	392	392	0
Eisenstein series	56	56	0

Trace form

\( 392 q - 29 q^{2} - 29 q^{3} - 79 q^{4} - 19 q^{5} - 33 q^{6} - 39 q^{7} - 71 q^{8} - 133 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(59, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
59.4.c.a	$59$	$4$	59.c	59.c	$29$	$392$	$14$	$3.481$		None		$2$	$0$	\(-29\)	\(-29\)	\(-19\)	\(-39\)		$\mathrm{SU}(2)[C_{29}]$