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

• Label: 828.2.u
• Level: $828$
• Weight: $2$
• Character orbit: 828.u
• Rep. character: $\chi_{828}(19,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $580$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.u (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	1520	620	900
Cusp forms	1360	580	780
Eisenstein series	160	40	120

Trace form

\( 580 q + 11 q^{2} - 3 q^{4} + 22 q^{5} + 14 q^{8} + O(q^{10}) \)

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.u.a	$828$	$2$	828.u	92.h	$22$	$100$	$10$	$6.612$		None		$4$	$0$	\(7\)	\(0\)	\(22\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$
828.2.u.b	$828$	$2$	828.u	92.h	$22$	$240$	$24$	$6.612$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$
828.2.u.c	$828$	$2$	828.u	92.h	$22$	$240$	$24$	$6.612$		None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

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

\( S_{2}^{\mathrm{old}}(828, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 3}\)