Space of modular forms of level 828, weight 3, and Character 828.p

• Label: 828.3.p
• Level: $828$
• Weight: $3$
• Character orbit: 828.p
• Rep. character: $\chi_{828}(229,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $432$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	828.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 207 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(432\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(828, [\chi])\).

	Total	New	Old
Modular forms	588	96	492
Cusp forms	564	96	468
Eisenstein series	24	0	24

Trace form

96 * q - 2 * q^3 + 6 * q^9 + 33 * q^23 + 246 * q^25 + 106 * q^27 - 42 * q^29 - 30 * q^31 - 90 * q^39 + 84 * q^41 - 84 * q^47 + 384 * q^49 - 132 * q^55 - 144 * q^59 + 215 * q^69 + 348 * q^71 + 64 * q^75 + 114 * q^77 + 454 * q^81 + 188 * q^87 + 446 * q^93 - 384 * q^95

Decomposition of \(S_{3}^{\mathrm{new}}(828, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
828.3.p.a	$828$	$3$	828.p	207.f	$6$	$96$	$48$	$22.561$		None		✓	✓	✓	828.3.p.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(828, [\chi])\) into lower level spaces

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