Space of modular forms of level 2224, weight 1, and Character 2224.e

• Label: 2224.1.e
• Level: $2224$
• Weight: $1$
• Character orbit: 2224.e
• Rep. character: $\chi_{2224}(833,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $280$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2224 = 2^{4} \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2224.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 139 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(280\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2224, [\chi])\).

	Total	New	Old
Modular forms	24	5	19
Cusp forms	18	4	14
Eisenstein series	6	1	5

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - q^{5} + q^{7} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2224, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2224.1.e.a	$2224$	$1$	2224.e	139.b	$2$	$1$	$1$	$1.110$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-139}) \)	None	✓		139.1.b.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$1$		\(q-q^{5}+q^{7}+q^{9}+q^{11}-q^{13}-q^{29}+\cdots\)
2224.1.e.b	$2224$	$1$	2224.e	139.b	$2$	$3$	$3$	$1.110$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-139}) \)	None	✓		556.1.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2224, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2224, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(139, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(278, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(556, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1112, [\chi])\)\(^{\oplus 2}\)