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

• Label: 648.2.i
• Level: $648$
• Weight: $2$
• Character orbit: 648.i
• Rep. character: $\chi_{648}(217,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $10$
• Sturm bound: $216$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(216\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	264	24	240
Cusp forms	168	24	144
Eisenstein series	96	0	96

Trace form

\( 24 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
648.2.i.a	$648$	$2$	648.i	9.c	$3$	$2$	$1$	$5.174$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
648.2.i.b	$648$	$2$	648.i	9.c	$3$	$2$	$1$	$5.174$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
648.2.i.c	$648$	$2$	648.i	9.c	$3$	$2$	$1$	$5.174$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
648.2.i.d	$648$	$2$	648.i	9.c	$3$	$2$	$1$	$5.174$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
648.2.i.e	$648$	$2$	648.i	9.c	$3$	$2$	$1$	$5.174$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
648.2.i.f	$648$	$2$	648.i	9.c	$3$	$2$	$1$	$5.174$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
648.2.i.g	$648$	$2$	648.i	9.c	$3$	$2$	$1$	$5.174$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
648.2.i.h	$648$	$2$	648.i	9.c	$3$	$2$	$1$	$5.174$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
648.2.i.i	$648$	$2$	648.i	9.c	$3$	$4$	$2$	$5.174$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
648.2.i.j	$648$	$2$	648.i	9.c	$3$	$4$	$2$	$5.174$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)