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

• Label: 828.2.o
• Level: $828$
• Weight: $2$
• Character orbit: 828.o
• Rep. character: $\chi_{828}(47,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $264$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	296	264	32
Cusp forms	280	264	16
Eisenstein series	16	0	16

Trace form

\( 264 q + 3 q^{6} + 4 q^{9} + O(q^{10}) \)

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.o.a	$828$	$2$	828.o	36.h	$6$	$132$	$66$	$6.612$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
828.2.o.b	$828$	$2$	828.o	36.h	$6$	$132$	$66$	$6.612$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(828, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)