Space of modular forms of level 6625, weight 2, and trivial character

• Label: 6625.2.a
• Level: $6625$
• Weight: $2$
• Character orbit: 6625.a
• Rep. character: $\chi_{6625}(1,\cdot)$
• Character field: $\Q$
• Dimension: $416$
• Newform subspaces: $12$
• Sturm bound: $1350$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 6625 = 5^{3} \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6625.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1350\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6625))\).

	Total	New	Old
Modular forms	684	416	268
Cusp forms	665	416	249
Eisenstein series	19	0	19

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

\(5\)	\(53\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(102\)
\(+\)	\(-\)	$-$	\(110\)
\(-\)	\(+\)	$-$	\(106\)
\(-\)	\(-\)	$+$	\(98\)
Plus space		\(+\)	\(200\)
Minus space		\(-\)	\(216\)

Trace form

\( 416 q + 416 q^{4} + 4 q^{6} + 424 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6625))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	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	53
6625.2.a.a	$6625$	$2$	6625.a	1.a	$1$	$2$	$2$	$52.901$	\(\Q(\sqrt{5}) \)	None	✓	✓	6625.2.a.a	$1$	$2$	\(-3\)	\(-2\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-2\beta q^{3}+3\beta q^{4}+(2+\cdots)q^{6}+\cdots\)
6625.2.a.b	$6625$	$2$	6625.a	1.a	$1$	$2$	$2$	$52.901$	\(\Q(\sqrt{5}) \)	None	✓	✓	6625.2.a.b	$1$	$0$	\(-1\)	\(4\)	\(0\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+2q^{3}+(-1+\beta )q^{4}-2\beta q^{6}+\cdots\)
6625.2.a.c	$6625$	$2$	6625.a	1.a	$1$	$2$	$2$	$52.901$	\(\Q(\sqrt{5}) \)	None	✓	✓	6625.2.a.b	$1$	$2$	\(1\)	\(-4\)	\(0\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2q^{3}+(-1+\beta )q^{4}-2\beta q^{6}+\cdots\)
6625.2.a.d	$6625$	$2$	6625.a	1.a	$1$	$2$	$2$	$52.901$	\(\Q(\sqrt{5}) \)	None	✓	✓	6625.2.a.a	$1$	$0$	\(3\)	\(2\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+2\beta q^{3}+3\beta q^{4}+(2+4\beta )q^{6}+\cdots\)
6625.2.a.e	$6625$	$2$	6625.a	1.a	$1$	$48$	$48$	$52.901$		None	✓	✓	6625.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(8\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6625.2.a.f	$6625$	$2$	6625.a	1.a	$1$	$48$	$48$	$52.901$		None	✓	✓	6625.2.a.e	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-8\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6625.2.a.g	$6625$	$2$	6625.a	1.a	$1$	$50$	$50$	$52.901$		None	✓	✓	6625.2.a.g	$1$	$1$	\(-14\)	\(-8\)	\(0\)	\(-28\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6625.2.a.h	$6625$	$2$	6625.a	1.a	$1$	$50$	$50$	$52.901$		None	✓	✓	6625.2.a.g	$1$	$0$	\(14\)	\(8\)	\(0\)	\(28\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6625.2.a.i	$6625$	$2$	6625.a	1.a	$1$	$52$	$52$	$52.901$		None	✓	✓	6625.2.a.i	$1$	$0$	\(-2\)	\(-7\)	\(0\)	\(-2\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6625.2.a.j	$6625$	$2$	6625.a	1.a	$1$	$52$	$52$	$52.901$		None	✓	✓	6625.2.a.i	$1$	$0$	\(2\)	\(7\)	\(0\)	\(2\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6625.2.a.k	$6625$	$2$	6625.a	1.a	$1$	$54$	$54$	$52.901$		None	✓	✓	6625.2.a.k	$1$	$1$	\(-14\)	\(-8\)	\(0\)	\(-28\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6625.2.a.l	$6625$	$2$	6625.a	1.a	$1$	$54$	$54$	$52.901$		None	✓	✓	6625.2.a.k	$1$	$0$	\(14\)	\(8\)	\(0\)	\(28\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6625))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6625)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(125))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(265))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1325))\)\(^{\oplus 2}\)