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

• Label: 975.2.cy
• Level: $975$
• Weight: $2$
• Character orbit: 975.cy
• Rep. character: $\chi_{975}(17,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $2176$
• 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.cy (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 975 \)
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	2304	0
Cusp forms	2176	2176	0
Eisenstein series	128	128	0

Trace form

2176 * q - 8 * q^3 - 20 * q^4 - 18 * q^6 - 48 * q^7 - 10 * q^9 - 24 * q^10 - 28 * q^12 - 16 * q^13 - 24 * q^15 - 260 * q^16 - 60 * q^19 - 40 * q^22 - 64 * q^25 - 8 * q^27 - 24 * q^28 - 10 * q^30 - 60 * q^33 + 26 * q^36 + 24 * q^37 - 60 * q^39 + 72 * q^40 + 38 * q^42 - 28 * q^43 - 84 * q^45 - 36 * q^46 - 152 * q^48 - 64 * q^51 - 28 * q^52 - 420 * q^54 + 20 * q^55 - 144 * q^58 - 12 * q^61 + 150 * q^63 + 80 * q^64 - 72 * q^66 - 96 * q^67 - 80 * q^69 - 120 * q^72 - 70 * q^75 - 96 * q^76 - 10 * q^78 - 80 * q^79 - 6 * q^81 + 8 * q^82 - 30 * q^84 - 144 * q^85 - 84 * q^87 + 128 * q^88 + 100 * q^90 - 24 * q^91 - 78 * q^93 - 300 * q^94 - 12 * q^97

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.cy.a	$975$	$2$	975.cy	975.by	$60$	$2176$	$136$	$7.785$		None		✓	✓	✓	975.2.cy.a	$8$	$0$	\(0\)	\(-8\)	\(0\)	\(-48\)		$\mathrm{SU}(2)[C_{60}]$