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

• Label: 975.1.cj
• Level: $975$
• Weight: $1$
• Character orbit: 975.cj
• Rep. character: $\chi_{975}(146,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $140$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	975.cj (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 975 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(140\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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	16

Trace form

16 * q - 6 * q^4 - 6 * q^6 - 8 * q^7 - 2 * q^9 + 6 * q^10 + 4 * q^13 + 2 * q^15 + 2 * q^19 + 8 * q^22 - 8 * q^24 + 4 * q^25 - 6 * q^28 + 6 * q^33 - 8 * q^34 - 4 * q^36 - 2 * q^37 + 4 * q^40 - 6 * q^42 + 4 * q^43 + 6 * q^46 - 16 * q^51 - 4 * q^52 + 6 * q^54 - 6 * q^55 - 8 * q^60 + 2 * q^61 - 2 * q^63 + 8 * q^64 + 4 * q^67 + 2 * q^69 - 12 * q^70 + 4 * q^73 + 4 * q^76 + 6 * q^78 + 2 * q^81 + 4 * q^82 + 2 * q^85 + 4 * q^88 - 8 * q^90 - 2 * q^91 - 2 * q^94 - 4 * q^96 - 4 * q^97

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.cj.a	$975$	$1$	975.cj	975.bj	$30$	$16$	$2$	$0.487$	\(\Q(\zeta_{60})\)	$A_{5}$	None	None		✓	✓	✓	975.1.cj.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$		\(q+(-\zeta_{60}^{11}+\zeta_{60}^{17})q^{2}+\zeta_{60}^{23}q^{3}+\cdots\)