Space of modular forms of level 29, weight 6, and Character 29.d

• Label: 29.6.d
• Level: $29$
• Weight: $6$
• Character orbit: 29.d
• Rep. character: $\chi_{29}(7,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $66$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	29.d (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(29, [\chi])\).

	Total	New	Old
Modular forms	78	78	0
Cusp forms	66	66	0
Eisenstein series	12	12	0

Trace form

\( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(29, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
29.6.d.a	$29$	$6$	29.d	29.d	$7$	$66$	$11$	$4.651$		None		$2$	$0$	\(-11\)	\(-5\)	\(29\)	\(17\)		$\mathrm{SU}(2)[C_{7}]$