Space of modular forms of level 224, weight 2, and Character 224.i

• Label: 224.2.i
• Level: $224$
• Weight: $2$
• Character orbit: 224.i
• Rep. character: $\chi_{224}(65,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $64$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(64\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(224, [\chi])\).

	Total	New	Old
Modular forms	80	16	64
Cusp forms	48	16	32
Eisenstein series	32	0	32

Trace form

\( 16 q - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(224, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
224.2.i.a	$224$	$2$	224.i	7.c	$3$	$4$	$2$	$1.789$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
224.2.i.b	$224$	$2$	224.i	7.c	$3$	$4$	$2$	$1.789$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
224.2.i.c	$224$	$2$	224.i	7.c	$3$	$4$	$2$	$1.789$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-3\beta _{2}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
224.2.i.d	$224$	$2$	224.i	7.c	$3$	$4$	$2$	$1.789$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(2\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{3}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

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