Space of modular forms of level 2891, weight 1, and Character 2891.c

• Label: 2891.1.c
• Level: $2891$
• Weight: $1$
• Character orbit: 2891.c
• Rep. character: $\chi_{2891}(589,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $7$
• Sturm bound: $280$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2891 = 7^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2891.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 59 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(280\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2891, [\chi])\).

	Total	New	Old
Modular forms	18	12	6
Cusp forms	10	7	3
Eisenstein series	8	5	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	7	0	0	0

Trace form

\( 7 q + q^{3} + 7 q^{4} + q^{5} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2891, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2891.1.c.a	$2891$	$1$	2891.c	59.b	$2$	$1$	$1$	$1.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)	$1$		\(q-2q^{3}+q^{4}+q^{5}+3q^{9}-2q^{12}+\cdots\)
2891.1.c.b	$2891$	$1$	2891.c	59.b	$2$	$1$	$1$	$1.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q-q^{3}+q^{4}-q^{5}-q^{12}+q^{15}+q^{16}+\cdots\)
2891.1.c.c	$2891$	$1$	2891.c	59.b	$2$	$1$	$1$	$1.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)	$1$		\(q-q^{3}+q^{4}+2q^{5}-q^{12}-2q^{15}+\cdots\)
2891.1.c.d	$2891$	$1$	2891.c	59.b	$2$	$1$	$1$	$1.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)	$1$		\(q+q^{3}+q^{4}-2q^{5}+q^{12}-2q^{15}+\cdots\)
2891.1.c.e	$2891$	$1$	2891.c	59.b	$2$	$1$	$1$	$1.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$		\(q+q^{3}+q^{4}+q^{5}+q^{12}+q^{15}+q^{16}+\cdots\)
2891.1.c.f	$2891$	$1$	2891.c	59.b	$2$	$1$	$1$	$1.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$		\(q+q^{3}+q^{4}+q^{5}+q^{12}+q^{15}+q^{16}+\cdots\)
2891.1.c.g	$2891$	$1$	2891.c	59.b	$2$	$1$	$1$	$1.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)	$1$		\(q+2q^{3}+q^{4}-q^{5}+3q^{9}+2q^{12}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2891, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2891, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 3}\)