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

• Label: 725.2.e
• Level: $725$
• Weight: $2$
• Character orbit: 725.e
• Rep. character: $\chi_{725}(157,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $86$
• 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.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
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	162	94	68
Cusp forms	138	86	52
Eisenstein series	24	8	16

Trace form

86 * q + 4 * q^3 - 82 * q^4 + 4 * q^7 + 94 * q^9 + 4 * q^11 + 8 * q^12 + 14 * q^13 + 16 * q^14 + 66 * q^16 - 44 * q^21 - 8 * q^22 + 4 * q^23 + 6 * q^26 + 4 * q^27 - 8 * q^28 - 28 * q^31 - 16 * q^34 - 154 * q^36 - 16 * q^37 - 8 * q^38 - 68 * q^39 - 30 * q^41 - 4 * q^42 - 12 * q^43 - 36 * q^44 - 8 * q^46 + 36 * q^47 - 4 * q^48 - 26 * q^52 - 14 * q^53 - 56 * q^56 - 12 * q^57 - 58 * q^58 - 18 * q^61 + 28 * q^62 + 60 * q^63 + 54 * q^64 + 20 * q^66 + 32 * q^67 - 12 * q^69 - 100 * q^76 - 56 * q^78 + 8 * q^79 + 190 * q^81 + 58 * q^82 + 60 * q^83 + 56 * q^84 + 12 * q^87 + 68 * q^88 - 62 * q^89 - 28 * q^92 - 8 * q^93 + 8 * q^97 - 34 * q^98 + 36 * 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.e.a	$725$	$2$	725.e	145.e	$4$	$4$	$2$	$5.789$	\(\Q(i, \sqrt{5})\)	None		✓			725.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}-3q^{4}+(-\beta _{2}+\beta _{3})q^{7}-\beta _{2}q^{8}+\cdots\)
725.2.e.b	$725$	$2$	725.e	145.e	$4$	$16$	$8$	$5.789$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			725.2.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{7}q^{2}+\beta _{9}q^{3}-\beta _{2}q^{4}+(\beta _{4}+\beta _{6}+\cdots)q^{6}+\cdots\)
725.2.e.c	$725$	$2$	725.e	145.e	$4$	$26$	$13$	$5.789$		None					145.2.e.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$
725.2.e.d	$725$	$2$	725.e	145.e	$4$	$40$	$20$	$5.789$		None		✓	✓		725.2.e.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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