Space of modular forms of level 648, weight 2, and Character 648.t

• Label: 648.2.t
• Level: $648$
• Weight: $2$
• Character orbit: 648.t
• Rep. character: $\chi_{648}(37,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $204$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 216 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(648, [\chi])\).

	Total	New	Old
Modular forms	684	228	456
Cusp forms	612	204	408
Eisenstein series	72	24	48

Trace form

204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(648, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
648.2.t.a	$648$	$2$	648.t	216.t	$18$	$204$	$34$	$5.174$		None			✓	✓	216.2.t.a	$4$	$0$	\(6\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(648, [\chi])\) into lower level spaces

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