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

• Label: 725.2.bi
• Level: $725$
• Weight: $2$
• Character orbit: 725.bi
• Rep. character: $\chi_{725}(3,\cdot)$
• Character field: $\Q(\zeta_{140})$
• Dimension: $3504$
• 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.bi (of order \(140\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 725 \)
Character field:			\(\Q(\zeta_{140})\)
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	3696	3696	0
Cusp forms	3504	3504	0
Eisenstein series	192	192	0

Trace form

3504 * q - 46 * q^2 - 50 * q^3 - 212 * q^4 - 56 * q^5 - 42 * q^6 - 40 * q^7 - 46 * q^8 + 68 * q^9 - 54 * q^10 - 36 * q^11 - 40 * q^12 - 42 * q^13 - 72 * q^14 - 56 * q^15 + 104 * q^16 - 60 * q^17 - 154 * q^18 - 80 * q^19 - 56 * q^20 - 66 * q^21 - 48 * q^22 - 40 * q^23 + 56 * q^24 + 58 * q^25 - 156 * q^26 + 88 * q^27 + 8 * q^28 - 80 * q^29 - 76 * q^30 - 16 * q^31 - 56 * q^32 - 56 * q^33 - 110 * q^34 - 96 * q^35 - 188 * q^36 - 68 * q^37 - 300 * q^38 - 72 * q^39 - 14 * q^40 - 16 * q^41 - 92 * q^42 - 132 * q^43 - 122 * q^44 - 80 * q^45 - 36 * q^46 - 32 * q^47 - 118 * q^48 + 124 * q^50 - 112 * q^51 - 136 * q^52 + 224 * q^53 - 50 * q^54 + 18 * q^56 + 12 * q^57 - 226 * q^58 - 120 * q^59 + 356 * q^60 - 266 * q^61 + 42 * q^62 - 228 * q^63 - 212 * q^64 - 44 * q^65 - 162 * q^66 - 88 * q^67 - 210 * q^68 - 72 * q^69 - 4 * q^70 - 42 * q^71 + 108 * q^72 + 64 * q^73 - 194 * q^75 - 112 * q^76 - 238 * q^77 - 120 * q^78 - 20 * q^79 + 740 * q^80 + 84 * q^81 - 66 * q^82 - 96 * q^83 - 356 * q^84 - 66 * q^85 + 640 * q^86 - 78 * q^87 + 80 * q^88 - 150 * q^89 - 230 * q^90 - 42 * q^91 - 56 * q^92 - 48 * q^93 - 50 * q^94 - 350 * q^95 - 102 * q^96 - 124 * q^97 - 470 * 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.bi.a	$725$	$2$	725.bi	725.ai	$140$	$3504$	$73$	$5.789$		None		✓	✓	✓	725.2.bi.a	$2$	$0$	\(-46\)	\(-50\)	\(-56\)	\(-40\)		$\mathrm{SU}(2)[C_{140}]$