Space of modular forms of level 440, weight 2, and Character 440.l

• Label: 440.2.l
• Level: $440$
• Weight: $2$
• Character orbit: 440.l
• Rep. character: $\chi_{440}(309,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(440, [\chi])\).

	Total	New	Old
Modular forms	76	60	16
Cusp forms	68	60	8
Eisenstein series	8	0	8

Trace form

\( 60 q + 4 q^{4} - 4 q^{6} + 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(440, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
440.2.l.a	$440$	$2$	440.l	40.f	$2$	$2$	$2$	$3.513$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(-4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
440.2.l.b	$440$	$2$	440.l	40.f	$2$	$2$	$2$	$3.513$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(4\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+i)q^{2}+2q^{3}+2iq^{4}+(1+2i)q^{5}+\cdots\)
440.2.l.c	$440$	$2$	440.l	40.f	$2$	$56$	$56$	$3.513$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)