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

• Label: 224.2.q
• Level: $224$
• Weight: $2$
• Character orbit: 224.q
• Rep. character: $\chi_{224}(47,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	80	20	60
Cusp forms	48	12	36
Eisenstein series	32	8	24

Trace form

\( 12 q + 6 q^{3} + O(q^{10}) \)

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.q.a	$224$	$2$	224.q	56.m	$6$	$12$	$6$	$1.789$	12.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{8}q^{3}+(-\beta _{4}-\beta _{7})q^{5}+(\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots\)

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

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