Space of modular forms of level 224, weight 4, and Character 224.i

• Label: 224.4.i
• Level: $224$
• Weight: $4$
• Character orbit: 224.i
• Rep. character: $\chi_{224}(65,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $5$
• Sturm bound: $128$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	224.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(128\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(224, [\chi])\).

	Total	New	Old
Modular forms	208	48	160
Cusp forms	176	48	128
Eisenstein series	32	0	32

Trace form

\( 48 q - 216 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(224, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
224.4.i.a	$224$	$4$	224.i	7.c	$3$	$4$	$2$	$13.216$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-8\beta _{1}-5\beta _{3})q^{7}+\cdots\)
224.4.i.b	$224$	$4$	224.i	7.c	$3$	$8$	$4$	$13.216$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7})q^{3}+(\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
224.4.i.c	$224$	$4$	224.i	7.c	$3$	$12$	$6$	$13.216$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-6\)	\(10\)	\(4\)	$2^{14}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2}+\beta _{7}-\beta _{8})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
224.4.i.d	$224$	$4$	224.i	7.c	$3$	$12$	$6$	$13.216$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{14}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{3}+(\beta _{1}+\beta _{6})q^{5}+(-\beta _{3}+\beta _{9}+\cdots)q^{7}+\cdots\)
224.4.i.e	$224$	$4$	224.i	7.c	$3$	$12$	$6$	$13.216$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(6\)	\(10\)	\(-4\)	$2^{14}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2}-\beta _{7}+\beta _{8})q^{3}+(-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)