Space of modular forms of level 828, weight 2, and Character 828.k

• Label: 828.2.k
• Level: $828$
• Weight: $2$
• Character orbit: 828.k
• Rep. character: $\chi_{828}(137,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 207 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(828, [\chi])\).

	Total	New	Old
Modular forms	300	48	252
Cusp forms	276	48	228
Eisenstein series	24	0	24

Trace form

\( 48 q - 2 q^{3} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(828, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
828.2.k.a	$828$	$2$	828.k	207.g	$6$	$48$	$24$	$6.612$		None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(828, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(828, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)