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

• Label: 725.2.o
• Level: $725$
• Weight: $2$
• Character orbit: 725.o
• Rep. character: $\chi_{725}(86,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $296$
• 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.o (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 725 \)
Character field:			\(\Q(\zeta_{10})\)
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	312	312	0
Cusp forms	296	296	0
Eisenstein series	16	16	0

Trace form

296 * q + 68 * q^4 - 6 * q^5 - 10 * q^6 - 24 * q^7 + 68 * q^9 - 10 * q^13 - 88 * q^16 - 2 * q^20 - 6 * q^22 + 6 * q^23 + 2 * q^25 - 42 * q^28 - 7 * q^29 - 52 * q^30 - 66 * q^33 - 38 * q^34 - 52 * q^35 - 68 * q^36 + 28 * q^38 - 50 * q^42 - 34 * q^45 + 288 * q^49 - 72 * q^51 + 92 * q^52 - 12 * q^53 + 24 * q^54 - 76 * q^57 - 60 * q^58 - 6 * q^59 + 10 * q^62 - 76 * q^63 + 48 * q^64 + 116 * q^65 - 62 * q^67 + 4 * q^71 + 76 * q^74 + 118 * q^78 - 186 * q^80 - 60 * q^81 + 28 * q^82 + 50 * q^83 + 56 * q^86 - 4 * q^87 - 66 * q^88 - 80 * q^91 + 10 * q^92 - 56 * q^93 - 58 * q^94 - 84 * q^96

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.o.a	$725$	$2$	725.o	725.o	$10$	$296$	$74$	$5.789$		None		✓	✓	✓	725.2.o.a	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(-24\)		$\mathrm{SU}(2)[C_{10}]$