Space of modular forms of level 2800, weight 1, and Character 2800.bf

• Label: 2800.1.bf
• Level: $2800$
• Weight: $1$
• Character orbit: 2800.bf
• Rep. character: $\chi_{2800}(349,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $480$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2800.bf (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 560 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(480\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2800, [\chi])\).

	Total	New	Old
Modular forms	36	20	16
Cusp forms	12	12	0
Eisenstein series	24	8	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + 12 q^{49} + 12 q^{56} + 12 q^{64} - 12 q^{74} - 12 q^{81}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2800, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2800.1.bf.a	$2800$	$1$	2800.bf	560.af	$4$	$2$	$1$	$1.397$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None					112.1.l.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{2}+q^{4}-q^{7}-q^{8}+i q^{9}+(-i-1)q^{11}+\cdots\)
2800.1.bf.b	$2800$	$1$	2800.bf	560.af	$4$	$2$	$1$	$1.397$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None					112.1.l.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$1$		\(q+q^{2}+q^{4}+q^{7}+q^{8}+i q^{9}+(-i-1)q^{11}+\cdots\)
2800.1.bf.c	$2800$	$1$	2800.bf	560.af	$4$	$4$	$2$	$1.397$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-7}) \)	None		✓			2800.1.z.b	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$1$		\(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+q^{7}+q^{8}+\cdots\)
2800.1.bf.d	$2800$	$1$	2800.bf	560.af	$4$	$4$	$2$	$1.397$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-7}) \)	None		✓			2800.1.z.b	$4$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$1$		\(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-q^{7}-q^{8}+\cdots\)