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

• Label: 725.2.be
• Level: $725$
• Weight: $2$
• Character orbit: 725.be
• Rep. character: $\chi_{725}(16,\cdot)$
• Character field: $\Q(\zeta_{35})$
• Dimension: $1728$
• 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.be (of order \(35\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 725 \)
Character field:			\(\Q(\zeta_{35})\)
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	1824	1824	0
Cusp forms	1728	1728	0
Eisenstein series	96	96	0

Trace form

1728 * q - 17 * q^2 - 15 * q^3 + 53 * q^4 - 24 * q^5 - 27 * q^6 - 48 * q^7 - 29 * q^8 + 49 * q^9 - 34 * q^10 - 15 * q^11 - 56 * q^12 - 11 * q^13 - 3 * q^14 - 26 * q^15 + 37 * q^16 - 64 * q^17 + 50 * q^18 - 3 * q^19 - 146 * q^20 - 9 * q^21 - 31 * q^22 - 3 * q^23 - 28 * q^24 + 24 * q^25 - 18 * q^26 - 72 * q^27 - 16 * q^28 - 20 * q^29 + 18 * q^30 - 3 * q^31 - 8 * q^32 - 51 * q^33 - 110 * q^34 + 38 * q^35 + 59 * q^36 + 63 * q^37 - 184 * q^38 - 27 * q^39 - 39 * q^40 - 42 * q^41 + 13 * q^42 + 36 * q^43 + 3 * q^44 + 22 * q^45 - 44 * q^46 + 3 * q^47 + 53 * q^48 - 272 * q^49 - 82 * q^50 + 34 * q^51 - 230 * q^52 - 93 * q^53 - 57 * q^54 - 28 * q^55 - 5 * q^56 - 156 * q^57 - 263 * q^58 + 132 * q^59 - 85 * q^60 - 115 * q^61 + 7 * q^62 + 47 * q^63 - 23 * q^64 + 98 * q^65 + 31 * q^66 - 23 * q^67 + 218 * q^68 - 35 * q^69 + 128 * q^70 - 88 * q^71 + 41 * q^72 + 85 * q^73 - 24 * q^74 - 18 * q^75 + 16 * q^76 + 105 * q^77 - 209 * q^78 - 31 * q^79 - 327 * q^80 + 93 * q^81 - 76 * q^82 - 71 * q^83 - 270 * q^84 + 159 * q^85 - 84 * q^86 - 147 * q^87 + 16 * q^88 + 45 * q^89 - 51 * q^90 - 91 * q^91 + 41 * q^92 - 112 * q^93 + 31 * q^94 + 70 * q^95 - 163 * q^96 + 149 * q^97 - 115 * q^98 - 216 * 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.be.a	$725$	$2$	725.be	725.ae	$35$	$1728$	$72$	$5.789$		None		✓	✓	✓	725.2.be.a	$4$	$0$	\(-17\)	\(-15\)	\(-24\)	\(-48\)		$\mathrm{SU}(2)[C_{35}]$