Space of modular forms of level 224, weight 3, and Character 224.r

• Label: 224.3.r
• Level: $224$
• Weight: $3$
• Character orbit: 224.r
• Rep. character: $\chi_{224}(95,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(224, [\chi])\).

	Total	New	Old
Modular forms	144	32	112
Cusp forms	112	32	80
Eisenstein series	32	0	32

Trace form

\( 32 q + 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(224, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
224.3.r.a	$224$	$3$	224.r	28.g	$6$	$4$	$2$	$6.104$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-18\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+5\zeta_{12}q^{3}-9\zeta_{12}^{2}q^{5}+(8\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots\)
224.3.r.b	$224$	$3$	224.r	28.g	$6$	$4$	$2$	$6.104$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-7\zeta_{12}^{3}q^{7}+\cdots\)
224.3.r.c	$224$	$3$	224.r	28.g	$6$	$12$	$6$	$6.104$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(\beta _{5}+\beta _{11})q^{5}+(\beta _{3}-\beta _{6}+\cdots)q^{7}+\cdots\)
224.3.r.d	$224$	$3$	224.r	28.g	$6$	$12$	$6$	$6.104$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(18\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{7}+\beta _{9}-\beta _{10})q^{3}+(-3\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)