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

• Label: 975.1.x
• Level: $975$
• Weight: $1$
• Character orbit: 975.x
• Rep. character: $\chi_{975}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $140$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	975.x (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(140\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	28	16	12
Cusp forms	4	4	0
Eisenstein series	24	12	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 2 q^{4} - 2 q^{9} - 2 q^{16} - 6 q^{19} + 2 q^{36} - 2 q^{39} + 4 q^{49} + 4 q^{61} - 4 q^{64} - 6 q^{76} + 4 q^{79} - 2 q^{81} + 6 q^{84} - 6 q^{91}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
975.1.x.a	$975$	$1$	975.x	39.h	$6$	$2$	$1$	$0.487$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			975.1.x.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-3\)	$1$		\(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+(-1-\zeta_{6})q^{7}+\cdots\)
975.1.x.b	$975$	$1$	975.x	39.h	$6$	$2$	$1$	$0.487$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			975.1.x.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(3\)	$1$		\(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)