Space of modular forms of level 1860, weight 1, and Character 1860.be

• Label: 1860.1.be
• Level: $1860$
• Weight: $1$
• Character orbit: 1860.be
• Rep. character: $\chi_{1860}(119,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1860.be (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1860 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1860, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	8	8	0
Eisenstein series	16	16	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 4 q^{4} - 6 q^{6} - 4 q^{9} - 2 q^{10} - 4 q^{16} - 4 q^{25} - 6 q^{34} + 2 q^{36} + 4 q^{40} + 4 q^{49} + 8 q^{64} + 8 q^{69} + 6 q^{76} - 4 q^{81} - 2 q^{90} - 12 q^{94} + 6 q^{96}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1860, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1860.1.be.a	$1860$	$1$	1860.be	1860.ae	$6$	$2$	$1$	$0.928$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.be.a	$4$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
1860.1.be.b	$1860$	$1$	1860.be	1860.ae	$6$	$2$	$1$	$0.928$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.be.a	$4$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1860.1.be.c	$1860$	$1$	1860.be	1860.ae	$6$	$2$	$1$	$0.928$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.be.a	$4$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
1860.1.be.d	$1860$	$1$	1860.be	1860.ae	$6$	$2$	$1$	$0.928$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.be.a	$4$	$0$	\(1\)	\(1\)	\(-1\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)