Space of modular forms of level 3789, weight 1, and Character 3789.i

• Label: 3789.1.i
• Level: $3789$
• Weight: $1$
• Character orbit: 3789.i
• Rep. character: $\chi_{3789}(1234,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $422$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3789 = 3^{2} \cdot 421 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3789.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 421 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(422\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3789, [\chi])\).

	Total	New	Old
Modular forms	10	4	6
Cusp forms	2	2	0
Eisenstein series	8	2	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3789, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3789.1.i.a	$3789$	$1$	3789.i	421.d	$4$	$2$	$1$	$1.891$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	3789.1.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{4}-iq^{7}+(-1+i)q^{13}-q^{16}+\cdots\)