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

• Label: 224.2.t
• Level: $224$
• Weight: $2$
• Character orbit: 224.t
• Rep. character: $\chi_{224}(81,\cdot)$
• 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.t (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 + 4 * q^7 + 20 * q^15 - 2 * q^17 - 2 * q^23 - 4 * q^25 - 10 * q^31 - 14 * q^33 - 4 * q^39 - 8 * q^41 - 30 * q^47 - 12 * q^49 - 4 * q^55 - 4 * q^57 - 44 * q^63 + 8 * q^65 - 32 * q^71 - 10 * q^73 + 22 * q^79 + 22 * q^81 + 20 * q^87 - 10 * q^89 + 34 * q^95 + 40 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
224.2.t.a	$224$	$2$	224.t	56.p	$6$	$12$	$6$	$1.789$	12.0.\(\cdots\).1	None			✓	✓	56.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{10}q^{3}+(-\beta _{4}+\beta _{7})q^{5}+(\beta _{8}-\beta _{9}+\cdots)q^{7}+\cdots\)

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

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