Space of modular forms of level 2028, weight 1, and Character 2028.v

• Label: 2028.1.v
• Level: $2028$
• Weight: $1$
• Character orbit: 2028.v
• Rep. character: $\chi_{2028}(587,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $364$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2028.v (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 156 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(364\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2028, [\chi])\).

	Total	New	Old
Modular forms	128	96	32
Cusp forms	16	16	0
Eisenstein series	112	80	32

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

\( 16 q + 8 q^{9} - 8 q^{16} + 8 q^{22} + 16 q^{40} + 16 q^{66} - 8 q^{81} + 8 q^{94}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2028, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2028.1.v.a	$2028$	$1$	2028.v	156.v	$12$	$4$	$1$	$1.012$	\(\Q(\zeta_{12})\)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None		✓			2028.1.l.a	$8$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
2028.1.v.b	$2028$	$1$	2028.v	156.v	$12$	$4$	$1$	$1.012$	\(\Q(\zeta_{12})\)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None		✓			2028.1.l.a	$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
2028.1.v.c	$2028$	$1$	2028.v	156.v	$12$	$4$	$1$	$1.012$	\(\Q(\zeta_{12})\)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None		✓			2028.1.l.a	$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
2028.1.v.d	$2028$	$1$	2028.v	156.v	$12$	$4$	$1$	$1.012$	\(\Q(\zeta_{12})\)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None		✓			2028.1.l.a	$8$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)