Space of modular forms of level 725, weight 2, and Character 725.s

• Label: 725.2.s
• Level: $725$
• Weight: $2$
• Character orbit: 725.s
• Rep. character: $\chi_{725}(17,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $584$
• Newform subspaces: $1$
• Sturm bound: $150$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.s (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 725 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(150\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(725, [\chi])\).

	Total	New	Old
Modular forms	616	616	0
Cusp forms	584	584	0
Eisenstein series	32	32	0

Trace form

584 * q - 4 * q^2 - 10 * q^3 - 142 * q^4 - 16 * q^7 + 8 * q^8 + 138 * q^9 - 4 * q^10 - 6 * q^11 - 10 * q^12 - 14 * q^13 - 22 * q^14 - 20 * q^15 - 146 * q^16 - 30 * q^17 + 48 * q^18 + 10 * q^19 - 36 * q^21 + 8 * q^22 - 16 * q^23 - 30 * q^25 - 26 * q^26 - 40 * q^27 + 8 * q^28 + 10 * q^29 - 36 * q^30 + 14 * q^31 - 48 * q^32 + 16 * q^34 + 16 * q^35 + 146 * q^36 - 80 * q^37 + 148 * q^38 - 22 * q^39 + 12 * q^40 + 34 * q^41 - 36 * q^42 + 68 * q^44 + 24 * q^45 - 6 * q^46 + 40 * q^47 + 10 * q^48 - 38 * q^50 - 46 * q^52 + 56 * q^53 - 20 * q^54 - 16 * q^55 + 80 * q^56 + 12 * q^57 + 32 * q^58 - 20 * q^59 - 110 * q^60 + 24 * q^61 - 28 * q^62 - 60 * q^63 - 142 * q^64 - 12 * q^65 - 180 * q^66 - 32 * q^67 + 148 * q^68 - 22 * q^69 + 152 * q^70 - 170 * q^72 - 46 * q^73 + 64 * q^75 + 12 * q^77 - 76 * q^78 - 50 * q^79 + 12 * q^80 - 126 * q^81 + 38 * q^82 + 40 * q^83 + 68 * q^84 - 170 * q^85 - 60 * q^86 + 80 * q^87 - 192 * q^88 + 50 * q^89 - 104 * q^90 + 28 * q^92 + 8 * q^93 - 20 * q^94 - 10 * q^95 - 60 * q^96 + 130 * q^97 + 20 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(725, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
725.2.s.a	$725$	$2$	725.s	725.s	$20$	$584$	$73$	$5.789$		None		✓	✓	✓	725.2.s.a	$2$	$0$	\(-4\)	\(-10\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{20}]$