Space of modular forms of level 2872, weight 1, and Character 2872.b

• Label: 2872.1.b
• Level: $2872$
• Weight: $1$
• Character orbit: 2872.b
• Rep. character: $\chi_{2872}(717,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $5$
• Sturm bound: $360$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2872 = 2^{3} \cdot 359 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2872.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2872 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(360\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2872, [\chi])\).

	Total	New	Old
Modular forms	25	25	0
Cusp forms	23	23	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	23	0	0	0

Trace form

\( 23 q + 4 q^{4} - 15 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2872, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2872.1.b.a	$2872$	$1$	2872.b	2872.b	$2$	$1$	$1$	$1.433$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-359}) \), \(\Q(\sqrt{-718}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-2q^{17}+\cdots\)
2872.1.b.b	$2872$	$1$	2872.b	2872.b	$2$	$1$	$1$	$1.433$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-718}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}+q^{9}-q^{13}+q^{16}+\cdots\)
2872.1.b.c	$2872$	$1$	2872.b	2872.b	$2$	$1$	$1$	$1.433$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-718}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}+q^{9}+q^{13}+q^{16}+\cdots\)
2872.1.b.d	$2872$	$1$	2872.b	2872.b	$2$	$2$	$2$	$1.433$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-718}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}-q^{8}+q^{9}-\beta q^{13}+q^{16}+\cdots\)
2872.1.b.e	$2872$	$1$	2872.b	2872.b	$2$	$18$	$18$	$1.433$	\(\Q(\zeta_{38})\)	$D_{38}$	\(\Q(\sqrt{-359}) \)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{38}^{13}q^{2}+(-\zeta_{38}^{8}-\zeta_{38}^{11})q^{3}+\cdots\)