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

• Label: 725.2.bd
• Level: $725$
• Weight: $2$
• Character orbit: 725.bd
• Rep. character: $\chi_{725}(43,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $516$
• Newform subspaces: $3$
• Sturm bound: $150$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.bd (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(150\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	972	564	408
Cusp forms	828	516	312
Eisenstein series	144	48	96

Trace form

516 * q + 14 * q^2 + 10 * q^3 + 82 * q^4 - 28 * q^6 + 10 * q^7 + 14 * q^8 - 94 * q^9 - 32 * q^11 + 20 * q^12 + 28 * q^13 - 16 * q^14 - 94 * q^16 - 84 * q^18 - 40 * q^21 + 22 * q^22 + 10 * q^23 - 56 * q^24 + 36 * q^26 - 32 * q^27 + 8 * q^28 - 56 * q^31 + 14 * q^32 + 14 * q^33 + 72 * q^34 - 42 * q^36 + 72 * q^37 + 120 * q^38 + 68 * q^39 + 2 * q^41 + 18 * q^42 - 2 * q^43 - 188 * q^44 - 20 * q^46 - 22 * q^47 - 38 * q^48 + 168 * q^49 - 28 * q^51 - 86 * q^52 - 56 * q^53 + 28 * q^56 + 12 * q^57 - 96 * q^58 - 10 * q^61 + 112 * q^62 - 158 * q^63 - 54 * q^64 - 48 * q^66 - 18 * q^67 - 140 * q^68 - 212 * q^69 - 28 * q^71 + 98 * q^72 + 84 * q^73 + 224 * q^74 + 72 * q^76 - 28 * q^77 - 70 * q^78 - 8 * q^79 - 218 * q^81 - 16 * q^82 - 46 * q^83 - 252 * q^84 - 68 * q^87 - 40 * q^88 + 62 * q^89 - 28 * q^91 + 14 * q^92 + 22 * q^93 - 168 * q^94 - 28 * q^96 + 76 * q^97 + 160 * q^98 + 188 * 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.bd.a	$725$	$2$	725.bd	145.t	$28$	$120$	$10$	$5.789$		None		✓			725.2.y.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$
725.2.bd.b	$725$	$2$	725.bd	145.t	$28$	$156$	$13$	$5.789$		None					145.2.o.a	$2$	$0$	\(14\)	\(10\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{28}]$
725.2.bd.c	$725$	$2$	725.bd	145.t	$28$	$240$	$20$	$5.789$		None		✓	✓		725.2.y.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$

Decomposition of \(S_{2}^{\mathrm{old}}(725, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(725, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)