Space of modular forms of level 544, weight 3, and Character 544.n

• Label: 544.3.n
• Level: $544$
• Weight: $3$
• Character orbit: 544.n
• Rep. character: $\chi_{544}(47,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $68$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	544.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(544, [\chi])\).

	Total	New	Old
Modular forms	304	76	228
Cusp forms	272	68	204
Eisenstein series	32	8	24

Trace form

\( 68 q + 4 q^{3} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(544, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
544.3.n.a	$544$	$3$	544.n	136.j	$4$	$4$	$2$	$14.823$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(-2\zeta_{8}+9\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
544.3.n.b	$544$	$3$	544.n	136.j	$4$	$64$	$32$	$14.823$		None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(544, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(544, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 2}\)