Space of modular forms of level 62, weight 6, and Character 62.d

• Label: 62.6.d
• Level: $62$
• Weight: $6$
• Character orbit: 62.d
• Rep. character: $\chi_{62}(33,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(62, [\chi])\).

	Total	New	Old
Modular forms	168	48	120
Cusp forms	152	48	104
Eisenstein series	16	0	16

Trace form

\( 48 q - 22 q^{3} - 192 q^{4} + 116 q^{5} + 288 q^{6} - 426 q^{7} - 772 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(62, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
62.6.d.a	$62$	$6$	62.d	31.d	$5$	$24$	$6$	$9.944$		None		$2$	$0$	\(-24\)	\(-20\)	\(120\)	\(-180\)		$\mathrm{SU}(2)[C_{5}]$
62.6.d.b	$62$	$6$	62.d	31.d	$5$	$24$	$6$	$9.944$		None		$2$	$0$	\(24\)	\(-2\)	\(-4\)	\(-246\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{6}^{\mathrm{old}}(62, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(62, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)