Space of modular forms of level 2583, weight 1, and Character 2583.ba

• Label: 2583.1.ba
• Level: $2583$
• Weight: $1$
• Character orbit: 2583.ba
• Rep. character: $\chi_{2583}(286,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $336$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2583 = 3^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2583.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2583 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(336\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2583, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	28	28	0
Eisenstein series	8	8	0

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

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

Trace form

\( 28 q - 14 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2583, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2583.1.ba.a	$2583$	$1$	2583.ba	2583.aa	$6$	$2$	$1$	$1.289$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-287}) \)	None		$4$	$0$	\(1\)	\(-2\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}^{2}q^{2}-q^{3}+\zeta_{6}^{2}q^{6}-\zeta_{6}^{2}q^{7}+\cdots\)
2583.1.ba.b	$2583$	$1$	2583.ba	2583.aa	$6$	$2$	$1$	$1.289$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-287}) \)	None		$4$	$0$	\(1\)	\(2\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}^{2}q^{6}+\zeta_{6}^{2}q^{7}+\cdots\)
2583.1.ba.c	$2583$	$1$	2583.ba	2583.aa	$6$	$12$	$6$	$1.289$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-287}) \)	None		$4$	$0$	\(-1\)	\(-2\)	\(0\)	\(-6\)	$1$		\(q+(-\zeta_{42}^{5}-\zeta_{42}^{9})q^{2}-\zeta_{42}^{3}q^{3}+\cdots\)
2583.1.ba.d	$2583$	$1$	2583.ba	2583.aa	$6$	$12$	$6$	$1.289$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-287}) \)	None		$4$	$0$	\(-1\)	\(2\)	\(0\)	\(6\)	$1$		\(q+(\zeta_{42}^{6}+\zeta_{42}^{8})q^{2}+\zeta_{42}^{9}q^{3}+(\zeta_{42}^{12}+\cdots)q^{4}+\cdots\)