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

• Label: 440.2.v
• Level: $440$
• Weight: $2$
• Character orbit: 440.v
• Rep. character: $\chi_{440}(153,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	160	36	124
Cusp forms	128	36	92
Eisenstein series	32	0	32

Trace form

\( 36 q + O(q^{10}) \)

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.v.a	$440$	$2$	440.v	55.e	$4$	$4$	$2$	$3.513$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(4\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{8})q^{3}+(-2-\zeta_{8})q^{5}+(2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
440.2.v.b	$440$	$2$	440.v	55.e	$4$	$32$	$16$	$3.513$		None		$4$	$0$	\(0\)	\(-4\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)