Space of modular forms of level 975, weight 2, and Character 975.cq

• Label: 975.2.cq
• Level: $975$
• Weight: $2$
• Character orbit: 975.cq
• Rep. character: $\chi_{975}(28,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $1120$
• Newform subspaces: $1$
• Sturm bound: $280$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.cq (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(280\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(975, [\chi])\).

	Total	New	Old
Modular forms	2304	1120	1184
Cusp forms	2176	1120	1056
Eisenstein series	128	0	128

Trace form

1120 * q - 140 * q^4 + 8 * q^5 - 16 * q^12 + 4 * q^15 + 140 * q^16 + 20 * q^17 - 32 * q^18 + 20 * q^19 + 100 * q^20 + 28 * q^22 + 8 * q^23 + 20 * q^25 - 40 * q^29 + 60 * q^32 + 8 * q^33 - 40 * q^34 + 60 * q^37 - 24 * q^40 - 140 * q^41 + 60 * q^42 + 12 * q^43 + 8 * q^45 - 24 * q^47 - 16 * q^48 - 560 * q^49 - 236 * q^50 - 88 * q^52 - 4 * q^53 + 148 * q^55 - 236 * q^58 + 48 * q^60 - 108 * q^62 + 280 * q^64 + 180 * q^65 - 12 * q^68 - 160 * q^70 + 12 * q^72 + 160 * q^73 - 60 * q^74 - 16 * q^75 - 48 * q^77 + 8 * q^78 - 164 * q^80 - 140 * q^81 - 228 * q^82 - 104 * q^83 + 104 * q^85 - 36 * q^87 - 336 * q^88 - 120 * q^89 + 12 * q^90 + 120 * q^91 + 64 * q^92 + 40 * q^94 + 100 * q^96 + 108 * q^97 + 56 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(975, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
975.2.cq.a	$975$	$2$	975.cq	325.ai	$60$	$1120$	$70$	$7.785$		None		✓	✓	✓	975.2.cq.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{60}]$

Decomposition of \(S_{2}^{\mathrm{old}}(975, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(975, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)