Space of modular forms of level 975, weight 1, and Character 975.bd

• Label: 975.1.bd
• Level: $975$
• Weight: $1$
• Character orbit: 975.bd
• Rep. character: $\chi_{975}(116,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $140$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	975.bd (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 975 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(140\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(975, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	16	16	0
Eisenstein series	16	16	0

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

\( 16 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(975, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
975.1.bd.a	$975$	$1$	975.bd	975.ad	$10$	$4$	$1$	$0.487$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-39}) \)	None		$4$	$0$	\(-3\)	\(-1\)	\(1\)	\(0\)	$1$		\(q+(-1+\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
975.1.bd.b	$975$	$1$	975.bd	975.ad	$10$	$4$	$1$	$0.487$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-39}) \)	None		$4$	$0$	\(3\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
975.1.bd.c	$975$	$1$	975.bd	975.ad	$10$	$8$	$2$	$0.487$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-39}) \)	None		$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}+\zeta_{20}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)