Space of modular forms of level 3481, weight 1, and Character 3481.d

• Label: 3481.1.d
• Level: $3481$
• Weight: $1$
• Character orbit: 3481.d
• Rep. character: $\chi_{3481}(506,\cdot)$
• Character field: $\Q(\zeta_{58})$
• Dimension: $84$
• Newform subspaces: $2$
• Sturm bound: $295$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3481 = 59^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3481.d (of order \(58\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 59 \)
Character field:			\(\Q(\zeta_{58})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(295\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3481, [\chi])\).

	Total	New	Old
Modular forms	924	868	56
Cusp forms	84	84	0
Eisenstein series	840	784	56

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	28	0	56	0

Trace form

\( 84 q - q^{3} + q^{4} + 3 q^{5} + 3 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3481, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3481.1.d.a	$3481$	$1$	3481.d	59.d	$58$	$28$	$1$	$1.737$	\(\Q(\zeta_{58})\)	$D_{3}$	\(\Q(\sqrt{-59}) \)	None		$56$	$0$	\(0\)	\(1\)	\(1\)	\(1\)	$1$		\(q+\zeta_{58}^{17}q^{3}-\zeta_{58}^{3}q^{4}+\zeta_{58}^{9}q^{5}+\cdots\)
3481.1.d.b	$3481$	$1$	3481.d	59.d	$58$	$56$	$2$	$1.737$	\(\mathbb{Q}[x]/(x^{56} - \cdots)\)	$S_{4}$	None	None		$56$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)	$1$		\(q-\beta _{31}q^{2}-\beta _{42}q^{3}-\beta _{4}q^{4}-\beta _{12}q^{5}+\cdots\)