Space of modular forms of level 441, weight 1, and Character 441.v

• Label: 441.1.v
• Level: $441$
• Weight: $1$
• Character orbit: 441.v
• Rep. character: $\chi_{441}(55,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	441.v (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(441, [\chi])\).

	Total	New	Old
Modular forms	30	12	18
Cusp forms	6	6	0
Eisenstein series	24	6	18

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + q^{4} + q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(441, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
441.1.v.a	$441$	$1$	441.v	49.f	$14$	$6$	$1$	$0.220$	\(\Q(\zeta_{14})\)	$D_{14}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q-\zeta_{14}^{4}q^{4}-\zeta_{14}^{2}q^{7}+(\zeta_{14}-\zeta_{14}^{3}+\cdots)q^{13}+\cdots\)