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

• Label: 440.2.c
• Level: $440$
• Weight: $2$
• Character orbit: 440.c
• Rep. character: $\chi_{440}(219,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 440 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

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

Trace form

\( 68 q - 4 q^{4} - 68 q^{9} + O(q^{10}) \)

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.c.a	$440$	$2$	440.c	440.c	$2$	$4$	$4$	$3.513$	\(\Q(\sqrt{-2}, \sqrt{5})\)	\(\Q(\sqrt{-10}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}+\beta _{3}q^{5}-2\beta _{1}q^{7}+\cdots\)
440.2.c.b	$440$	$2$	440.c	440.c	$2$	$8$	$8$	$3.513$	8.0.\(\cdots\).19	\(\Q(\sqrt{-55}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{2}-\beta _{5})q^{5}+\cdots\)
440.2.c.c	$440$	$2$	440.c	440.c	$2$	$56$	$56$	$3.513$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$