Space of modular forms of level 648, weight 3, and Character 648.h

• Label: 648.3.h
• Level: $648$
• Weight: $3$
• Character orbit: 648.h
• Rep. character: $\chi_{648}(485,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $2$
• Sturm bound: $324$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	648.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(324\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(648, [\chi])\).

	Total	New	Old
Modular forms	228	100	128
Cusp forms	204	92	112
Eisenstein series	24	8	16

Trace form

92 * q + 2 * q^4 + 4 * q^7 + 4 * q^10 + 14 * q^16 + 46 * q^22 + 384 * q^25 - 56 * q^28 + 4 * q^31 + 6 * q^34 - 8 * q^40 + 36 * q^46 + 480 * q^49 + 84 * q^52 + 92 * q^55 + 232 * q^58 - 262 * q^64 + 44 * q^70 - 8 * q^73 - 366 * q^76 + 388 * q^79 - 66 * q^82 - 98 * q^88 + 132 * q^94 + 4 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(648, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
648.3.h.a	$648$	$3$	648.h	24.h	$2$	$44$	$44$	$17.657$		None					72.3.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$
648.3.h.b	$648$	$3$	648.h	24.h	$2$	$48$	$48$	$17.657$		None		✓	✓		648.3.h.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(648, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(648, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)