Space of modular forms of level 880, weight 1, and Character 880.i

• Label: 880.1.i
• Level: $880$
• Weight: $1$
• Character orbit: 880.i
• Rep. character: $\chi_{880}(769,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	880.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(880, [\chi])\).

	Total	New	Old
Modular forms	26	5	21
Cusp forms	14	3	11
Eisenstein series	12	2	10

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

\( 3 q - 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(880, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
880.1.i.a	$880$	$1$	880.i	55.d	$2$	$1$	$1$	$0.439$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-q^{5}+q^{9}+q^{11}+q^{25}+2q^{31}+\cdots\)
880.1.i.b	$880$	$1$	880.i	55.d	$2$	$2$	$2$	$0.439$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(-\zeta_{6}-\zeta_{6}^{2})q^{3}-\zeta_{6}^{2}q^{5}+(-1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(880, [\chi]) \cong \)