Space of modular forms of level 25, weight 24, and trivial character

• Label: 25.24.a
• Level: $25$
• Weight: $24$
• Character orbit: 25.a
• Rep. character: $\chi_{25}(1,\cdot)$
• Character field: $\Q$
• Dimension: $35$
• Newform subspaces: $6$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(25))\).

	Total	New	Old
Modular forms	61	38	23
Cusp forms	55	35	20
Eisenstein series	6	3	3

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
\(+\)	\(17\)
\(-\)	\(18\)

Trace form

\( 35 q - 966 q^{2} + 6628 q^{3} + 139913590 q^{4} + 588032010 q^{6} + 4802578344 q^{7} + 54346119960 q^{8} + 1140870211815 q^{9} + O(q^{10}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.24.a.a	$25$	$24$	25.a	1.a	$1$	$2$	$2$	$83.801$	\(\Q(\sqrt{144169}) \)	None	✓	$1$	$0$	\(-1080\)	\(-339480\)	\(0\)	\(1359184400\)		$+$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-540-\beta )q^{2}+(-169740+48\beta )q^{3}+\cdots\)
25.24.a.b	$25$	$24$	25.a	1.a	$1$	$3$	$3$	$83.801$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(-666\)	\(139428\)	\(0\)	\(2432683344\)		$+$	$+$	$2^{3}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-222-\beta _{1})q^{2}+(46476-2^{6}\beta _{1}+\cdots)q^{3}+\cdots\)
25.24.a.c	$25$	$24$	25.a	1.a	$1$	$4$	$4$	$83.801$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(780\)	\(206680\)	\(0\)	\(1010710600\)		$+$	$+$	$2^{8}\cdot 3\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(195+\beta _{1})q^{2}+(51670+39\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
25.24.a.d	$25$	$24$	25.a	1.a	$1$	$8$	$8$	$83.801$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-3015\)	\(-181240\)	\(0\)	\(1728469600\)		$-$	$-$	$2^{19}\cdot 3^{5}\cdot 5^{14}$	$\mathrm{SU}(2)$	\(q+(-377+\beta _{1})q^{2}+(-22656+9\beta _{1}+\cdots)q^{3}+\cdots\)
25.24.a.e	$25$	$24$	25.a	1.a	$1$	$8$	$8$	$83.801$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(3015\)	\(181240\)	\(0\)	\(-1728469600\)		$+$	$+$	$2^{19}\cdot 3^{5}\cdot 5^{14}$	$\mathrm{SU}(2)$	\(q+(377-\beta _{1})q^{2}+(22656-9\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
25.24.a.f	$25$	$24$	25.a	1.a	$1$	$10$	$10$	$83.801$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$2^{34}\cdot 3^{12}\cdot 5^{24}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-18\beta _{1}-\beta _{4})q^{3}+(4127268+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)