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

• Label: 725.2.p
• Level: $725$
• Weight: $2$
• Character orbit: 725.p
• Rep. character: $\chi_{725}(149,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $264$
• Newform subspaces: $4$
• Sturm bound: $150$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.p (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 4 \)
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	480	288	192
Cusp forms	408	264	144
Eisenstein series	72	24	48

Trace form

\( 264 q - 34 q^{4} - 34 q^{6} - 34 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
725.2.p.a	$725$	$2$	725.p	145.l	$14$	$24$	$4$	$5.789$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$
725.2.p.b	$725$	$2$	725.p	145.l	$14$	$48$	$8$	$5.789$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$
725.2.p.c	$725$	$2$	725.p	145.l	$14$	$72$	$12$	$5.789$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$
725.2.p.d	$725$	$2$	725.p	145.l	$14$	$120$	$20$	$5.789$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$

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

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