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

• Label: 725.2.r
• Level: $725$
• Weight: $2$
• Character orbit: 725.r
• Rep. character: $\chi_{725}(24,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $252$
• Newform subspaces: $5$
• Sturm bound: $150$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.r (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(150\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	492	276	216
Cusp forms	420	252	168
Eisenstein series	72	24	48

Trace form

252 * q + 48 * q^4 + 22 * q^6 + 60 * q^9 - 18 * q^11 + 10 * q^14 - 32 * q^16 + 2 * q^19 + 30 * q^21 - 98 * q^24 - 32 * q^26 - 8 * q^29 + 2 * q^31 + 56 * q^34 - 6 * q^36 + 26 * q^39 - 4 * q^41 - 134 * q^44 - 44 * q^46 - 44 * q^49 - 44 * q^51 - 30 * q^54 - 4 * q^56 + 160 * q^59 - 34 * q^61 - 12 * q^64 + 166 * q^66 - 58 * q^69 - 52 * q^71 - 134 * q^74 - 146 * q^76 - 6 * q^79 - 148 * q^81 + 382 * q^84 - 356 * q^86 + 42 * q^89 + 30 * q^91 + 92 * q^94 - 270 * q^96 - 256 * 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.r.a	$725$	$2$	725.r	145.n	$14$	$12$	$2$	$5.789$	\(\Q(\zeta_{28})\)	None		✓			725.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(\zeta_{28}^{3}-\zeta_{28}^{5}+\zeta_{28}^{7}-\zeta_{28}^{9})q^{2}+\cdots\)
725.2.r.b	$725$	$2$	725.r	145.n	$14$	$12$	$2$	$5.789$	\(\Q(\zeta_{28})\)	None					29.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-\zeta_{28}^{3}+\zeta_{28}^{9})q^{2}+(-\zeta_{28}^{7}-\zeta_{28}^{11})q^{3}+\cdots\)
725.2.r.c	$725$	$2$	725.r	145.n	$14$	$48$	$8$	$5.789$		None					145.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$
725.2.r.d	$725$	$2$	725.r	145.n	$14$	$72$	$12$	$5.789$		None					145.2.k.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$
725.2.r.e	$725$	$2$	725.r	145.n	$14$	$108$	$18$	$5.789$		None		✓	✓		725.2.l.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$

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

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