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

• Label: 1860.1.df
• Level: $1860$
• Weight: $1$
• Character orbit: 1860.df
• Rep. character: $\chi_{1860}(179,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $32$
• 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.df (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1860 \)
Character field:			\(\Q(\zeta_{30})\)
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	96	96	0
Cusp forms	32	32	0
Eisenstein series	64	64	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

32 * q + 4 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 4 * q^16 - 16 * q^25 + 6 * q^34 - 2 * q^36 - 4 * q^40 - 10 * q^46 - 4 * q^49 - 10 * q^54 + 10 * q^60 - 8 * q^64 + 12 * q^69 + 4 * q^76 + 4 * q^81 + 2 * q^90 - 8 * q^94 - 6 * q^96

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.df.a	$1860$	$1$	1860.df	1860.cf	$30$	$8$	$1$	$0.928$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.df.a	$4$	$0$	\(-1\)	\(-1\)	\(-4\)	\(0\)	$1$		\(q-\zeta_{30}^{8}q^{2}-\zeta_{30}^{14}q^{3}-\zeta_{30}q^{4}+\cdots\)
1860.1.df.b	$1860$	$1$	1860.df	1860.cf	$30$	$8$	$1$	$0.928$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.df.a	$4$	$0$	\(-1\)	\(1\)	\(-4\)	\(0\)	$1$		\(q-\zeta_{30}^{4}q^{2}+\zeta_{30}^{14}q^{3}+\zeta_{30}^{8}q^{4}+\cdots\)
1860.1.df.c	$1860$	$1$	1860.df	1860.cf	$30$	$8$	$1$	$0.928$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.df.a	$4$	$0$	\(1\)	\(-1\)	\(4\)	\(0\)	$1$		\(q+\zeta_{30}^{4}q^{2}-\zeta_{30}^{14}q^{3}+\zeta_{30}^{8}q^{4}+\cdots\)
1860.1.df.d	$1860$	$1$	1860.df	1860.cf	$30$	$8$	$1$	$0.928$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-15}) \)	None		✓			1860.1.df.a	$4$	$0$	\(1\)	\(1\)	\(4\)	\(0\)	$1$		\(q+\zeta_{30}^{8}q^{2}+\zeta_{30}^{14}q^{3}-\zeta_{30}q^{4}+\cdots\)