Space of modular forms of level 29, weight 13, and Character 29.c

• Label: 29.13.c
• Level: $29$
• Weight: $13$
• Character orbit: 29.c
• Rep. character: $\chi_{29}(12,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $58$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(29, [\chi])\).

	Total	New	Old
Modular forms	62	62	0
Cusp forms	58	58	0
Eisenstein series	4	4	0

Trace form

\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8} + O(q^{10}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(29, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
29.13.c.a	$29$	$13$	29.c	29.c	$4$	$58$	$29$	$26.506$		None		$2$	$0$	\(88\)	\(-2\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$