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

• Label: 725.2.b
• Level: $725$
• Weight: $2$
• Character orbit: 725.b
• Rep. character: $\chi_{725}(349,\cdot)$
• Character field: $\Q$
• Dimension: $42$
• Newform subspaces: $7$
• Sturm bound: $150$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(150\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	82	42	40
Cusp forms	70	42	28
Eisenstein series	12	0	12

Trace form

\( 42 q - 34 q^{4} - 8 q^{6} - 46 q^{9} + O(q^{10}) \)

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.b.a	$725$	$2$	725.b	5.b	$2$	$2$	$2$	$5.789$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+2iq^{7}+3iq^{8}+3q^{9}+\cdots\)
725.2.b.b	$725$	$2$	725.b	5.b	$2$	$4$	$4$	$5.789$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
725.2.b.c	$725$	$2$	725.b	5.b	$2$	$4$	$4$	$5.789$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
725.2.b.d	$725$	$2$	725.b	5.b	$2$	$6$	$6$	$5.789$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-2-\beta _{3}+\cdots)q^{4}+\cdots\)
725.2.b.e	$725$	$2$	725.b	5.b	$2$	$6$	$6$	$5.789$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{6}+\cdots\)
725.2.b.f	$725$	$2$	725.b	5.b	$2$	$10$	$10$	$5.789$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
725.2.b.g	$725$	$2$	725.b	5.b	$2$	$10$	$10$	$5.789$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{7})q^{3}+(-1+\beta _{5}+\cdots)q^{4}+\cdots\)

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

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