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

• Label: 828.2.e
• Level: $828$
• Weight: $2$
• Character orbit: 828.e
• Rep. character: $\chi_{828}(91,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	152	62	90
Cusp forms	136	58	78
Eisenstein series	16	4	12

Trace form

\( 58 q - 8 q^{4} - 3 q^{8} + O(q^{10}) \)

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.e.a	$828$	$2$	828.e	92.b	$2$	$4$	$4$	$6.612$	\(\Q(i, \sqrt{14})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}+\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots\)
828.2.e.b	$828$	$2$	828.e	92.b	$2$	$6$	$6$	$6.612$	6.0.8869743.1	\(\Q(\sqrt{-23}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{5}q^{2}+\beta _{3}q^{4}+(2-\beta _{2})q^{8}+(\beta _{1}+\cdots)q^{13}+\cdots\)
828.2.e.c	$828$	$2$	828.e	92.b	$2$	$8$	$8$	$6.612$	8.0.\(\cdots\).2	\(\Q(\sqrt{-69}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}-2q^{4}-\beta _{4}q^{5}-\beta _{5}q^{7}-2\beta _{2}q^{8}+\cdots\)
828.2.e.d	$828$	$2$	828.e	92.b	$2$	$8$	$8$	$6.612$	8.0.3317760000.6	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{4}+\beta _{6}q^{7}+(-\beta _{1}-2\beta _{7})q^{8}+\cdots\)
828.2.e.e	$828$	$2$	828.e	92.b	$2$	$8$	$8$	$6.612$	8.0.157351936.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{3})q^{2}+(2-\beta _{1})q^{4}-2\beta _{6}q^{5}+\cdots\)
828.2.e.f	$828$	$2$	828.e	92.b	$2$	$24$	$24$	$6.612$		None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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