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

• Label: 725.2.d
• Level: $725$
• Weight: $2$
• Character orbit: 725.d
• Rep. character: $\chi_{725}(724,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q\)
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	80	48	32
Cusp forms	68	44	24
Eisenstein series	12	4	8

Trace form

44 * q + 48 * q^4 - 8 * q^6 + 48 * q^9 + 48 * q^16 - 64 * q^24 - 12 * q^29 - 12 * q^34 + 40 * q^36 + 4 * q^49 - 4 * q^51 - 28 * q^54 - 44 * q^59 + 68 * q^64 - 68 * q^71 - 16 * q^74 + 52 * q^81 - 80 * q^86 - 68 * q^91 - 56 * q^94 - 60 * q^96

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.d.a	$725$	$2$	725.d	145.d	$2$	$4$	$4$	$5.789$	\(\Q(i, \sqrt{5})\)	None					29.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{3}q^{3}+3q^{4}+5q^{6}-2\beta _{1}q^{7}+\cdots\)
725.2.d.b	$725$	$2$	725.d	145.d	$2$	$8$	$8$	$5.789$	\(\Q(\zeta_{24})\)	None					145.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{6} q^{2}+(-\beta_{6}+\beta_{3})q^{3}+\beta_{2} q^{4}+\cdots\)
725.2.d.c	$725$	$2$	725.d	145.d	$2$	$12$	$12$	$5.789$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					145.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(\beta _{5}-\beta _{7})q^{3}+(1+\beta _{4})q^{4}+\cdots\)
725.2.d.d	$725$	$2$	725.d	145.d	$2$	$20$	$20$	$5.789$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		725.2.c.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{16}q^{3}+(1-\beta _{9})q^{4}+(1+\cdots)q^{6}+\cdots\)

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

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