Space of modular forms of level 1148, weight 1, and Character 1148.bc

• Label: 1148.1.bc
• Level: $1148$
• Weight: $1$
• Character orbit: 1148.bc
• Rep. character: $\chi_{1148}(461,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1148.bc (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 287 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1148, [\chi])\).

	Total	New	Old
Modular forms	32	8	24
Cusp forms	8	8	0
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	0	8

Trace form

\( 8 q - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1148, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1148.1.bc.a	$1148$	$1$	1148.bc	287.o	$10$	$8$	$2$	$0.573$	\(\Q(\zeta_{20})\)	$A_{5}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{20}^{5}q^{3}-\zeta_{20}q^{5}-\zeta_{20}^{2}q^{7}+(\zeta_{20}^{2}+\cdots)q^{11}+\cdots\)