Space of modular forms of level 625, weight 8, and trivial character

• Label: 625.8.a
• Level: $625$
• Weight: $8$
• Character orbit: 625.a
• Rep. character: $\chi_{625}(1,\cdot)$
• Character field: $\Q$
• Dimension: $272$
• Newform subspaces: $7$
• Sturm bound: $500$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	625.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(500\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(625))\).

	Total	New	Old
Modular forms	453	288	165
Cusp forms	423	272	151
Eisenstein series	30	16	14

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)	Dim
\(+\)	\(138\)
\(-\)	\(134\)

Trace form

\( 272 q + 16896 q^{4} + 4 q^{6} + 186624 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(625))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5
625.8.a.a	$625$	$8$	625.a	1.a	$1$	$22$	$22$	$195.241$		None	✓	$1$	$1$	\(-23\)	\(-121\)	\(0\)	\(-843\)		$-$	$-$		$\mathrm{SU}(2)$
625.8.a.b	$625$	$8$	625.a	1.a	$1$	$22$	$22$	$195.241$		None	✓	$1$	$0$	\(23\)	\(121\)	\(0\)	\(843\)		$+$	$+$		$\mathrm{SU}(2)$
625.8.a.c	$625$	$8$	625.a	1.a	$1$	$34$	$34$	$195.241$		None	✓	$1$	$0$	\(-17\)	\(-14\)	\(0\)	\(-867\)		$+$	$+$		$\mathrm{SU}(2)$
625.8.a.d	$625$	$8$	625.a	1.a	$1$	$34$	$34$	$195.241$		None	✓	$1$	$0$	\(17\)	\(14\)	\(0\)	\(867\)		$+$	$+$		$\mathrm{SU}(2)$
625.8.a.e	$625$	$8$	625.a	1.a	$1$	$48$	$48$	$195.241$		None	✓	$1$	$1$	\(-25\)	\(-95\)	\(0\)	\(-4030\)		$-$	$-$		$\mathrm{SU}(2)$
625.8.a.f	$625$	$8$	625.a	1.a	$1$	$48$	$48$	$195.241$		None	✓	$1$	$0$	\(25\)	\(95\)	\(0\)	\(4030\)		$+$	$+$		$\mathrm{SU}(2)$
625.8.a.g	$625$	$8$	625.a	1.a	$1$	$64$	$64$	$195.241$		None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(625))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(625)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(125))\)\(^{\oplus 2}\)