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

• Label: 1860.1.bt
• Level: $1860$
• Weight: $1$
• Character orbit: 1860.bt
• Rep. character: $\chi_{1860}(959,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• 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.bt (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1860 \)
Character field:			\(\Q(\zeta_{10})\)
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	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q - 4 q^{4} - 4 q^{9} + 4 q^{10} - 4 q^{16} + 16 q^{25} - 4 q^{36} + 4 q^{40} + 10 q^{46} + 4 q^{49} + 10 q^{54} - 10 q^{60} - 4 q^{64} - 12 q^{69} - 10 q^{76} - 4 q^{81} + 4 q^{90} + 20 q^{94}+O(q^{100}) \)

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.bt.a	$1860$	$1$	1860.bt	1860.at	$10$	$4$	$1$	$0.928$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.bt.a	$4$	$0$	\(-1\)	\(-1\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{10}^{2}q^{2}-\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}-q^{5}+\cdots\)
1860.1.bt.b	$1860$	$1$	1860.bt	1860.at	$10$	$4$	$1$	$0.928$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.bt.a	$4$	$0$	\(-1\)	\(1\)	\(-4\)	\(0\)	$1$		\(q-\zeta_{10}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}-q^{5}+\cdots\)
1860.1.bt.c	$1860$	$1$	1860.bt	1860.at	$10$	$4$	$1$	$0.928$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.bt.a	$4$	$0$	\(1\)	\(-1\)	\(4\)	\(0\)	$1$		\(q+\zeta_{10}q^{2}-\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}+q^{5}+\cdots\)
1860.1.bt.d	$1860$	$1$	1860.bt	1860.at	$10$	$4$	$1$	$0.928$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.bt.a	$4$	$0$	\(1\)	\(1\)	\(4\)	\(0\)	$1$		\(q-\zeta_{10}^{2}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}+q^{5}+\cdots\)