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

• Label: 725.2.c
• Level: $725$
• Weight: $2$
• Character orbit: 725.c
• Rep. character: $\chi_{725}(376,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $8$
• Sturm bound: $150$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(150\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	82	50	32
Cusp forms	70	44	26
Eisenstein series	12	6	6

Trace form

44 * q - 40 * q^4 - 6 * q^6 - 34 * q^9 - 2 * q^13 + 16 * q^16 - 6 * q^22 + 8 * q^23 + 14 * q^24 + 56 * q^28 + 12 * q^29 - 26 * q^33 - 28 * q^34 - 18 * q^36 - 32 * q^38 + 20 * q^42 + 28 * q^49 + 24 * q^51 - 2 * q^52 - 10 * q^53 + 86 * q^54 - 56 * q^57 + 20 * q^58 - 16 * q^59 - 10 * q^62 - 4 * q^63 - 68 * q^64 + 4 * q^67 + 12 * q^71 + 4 * q^74 + 18 * q^78 + 36 * q^81 + 68 * q^82 + 48 * q^83 - 66 * q^86 - 44 * q^87 + 14 * q^88 + 40 * q^91 + 24 * q^92 - 6 * q^93 - 34 * q^94 - 26 * 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.c.a	$725$	$2$	725.c	29.b	$2$	$2$	$2$	$5.789$	\(\Q(\sqrt{-5}) \)	None					145.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-3q^{4}-2q^{7}-\beta q^{8}+3q^{9}+\cdots\)
725.2.c.b	$725$	$2$	725.c	29.b	$2$	$2$	$2$	$5.789$	\(\Q(\sqrt{-5}) \)	None					145.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-3q^{4}+2q^{7}-\beta q^{8}+3q^{9}+\cdots\)
725.2.c.c	$725$	$2$	725.c	29.b	$2$	$2$	$2$	$5.789$	\(\Q(\sqrt{-5}) \)	None					29.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-\beta q^{3}-3q^{4}+5q^{6}-2q^{7}+\cdots\)
725.2.c.d	$725$	$2$	725.c	29.b	$2$	$4$	$4$	$5.789$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None					145.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
725.2.c.e	$725$	$2$	725.c	29.b	$2$	$6$	$6$	$5.789$	6.0.16516096.1	None					145.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
725.2.c.f	$725$	$2$	725.c	29.b	$2$	$8$	$8$	$5.789$	8.0.1731891456.1	None					145.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}-\beta _{5}q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
725.2.c.g	$725$	$2$	725.c	29.b	$2$	$10$	$10$	$5.789$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			725.2.c.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
725.2.c.h	$725$	$2$	725.c	29.b	$2$	$10$	$10$	$5.789$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			725.2.c.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(725, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)