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

• Label: 440.2.t
• Level: $440$
• Weight: $2$
• Character orbit: 440.t
• Rep. character: $\chi_{440}(197,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $136$
• 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.t (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 440 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	152	152	0
Cusp forms	136	136	0
Eisenstein series	16	16	0

Trace form

\( 136 q + O(q^{10}) \)

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.t.a	$440$	$2$	440.t	440.t	$4$	$4$	$2$	$3.513$	\(\Q(i, \sqrt{10})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots\)
440.2.t.b	$440$	$2$	440.t	440.t	$4$	$4$	$2$	$3.513$	\(\Q(i, \sqrt{10})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
440.2.t.c	$440$	$2$	440.t	440.t	$4$	$128$	$64$	$3.513$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$