Space of modular forms of level 25, weight 22, and trivial character

• Label: 25.22.a
• Level: $25$
• Weight: $22$
• Character orbit: 25.a
• Rep. character: $\chi_{25}(1,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $6$
• Sturm bound: $55$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(55\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(25))\).

	Total	New	Old
Modular forms	55	35	20
Cusp forms	49	32	17
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.
\(+\)	\(15\)
\(-\)	\(17\)

Trace form

\( 32 q - 1310 q^{2} - 6590 q^{3} + 32915734 q^{4} + 32120394 q^{6} - 428951550 q^{7} - 7470710280 q^{8} + 80388051186 q^{9} + O(q^{10}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.22.a.a	$25$	$22$	25.a	1.a	$1$	$1$	$1$	$69.869$	\(\Q\)	None	✓	$1$	$1$	\(288\)	\(128844\)	\(0\)	\(768078808\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+288q^{2}+128844q^{3}-2014208q^{4}+\cdots\)
25.22.a.b	$25$	$22$	25.a	1.a	$1$	$3$	$3$	$69.869$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(1312\)	\(-52194\)	\(0\)	\(-684416558\)		$+$	$+$	$2^{7}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(437-\beta _{1})q^{2}+(-17400-8\beta _{1}+\cdots)q^{3}+\cdots\)
25.22.a.c	$25$	$22$	25.a	1.a	$1$	$4$	$4$	$69.869$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(-2910\)	\(-83240\)	\(0\)	\(-512613800\)		$+$	$+$	$2^{6}\cdot 3\cdot 5^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-728+\beta _{1})q^{2}+(-20803-14\beta _{1}+\cdots)q^{3}+\cdots\)
25.22.a.d	$25$	$22$	25.a	1.a	$1$	$7$	$7$	$69.869$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-737\)	\(-50381\)	\(0\)	\(-817782442\)		$+$	$+$	$2^{13}\cdot 3^{3}\cdot 5^{10}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(-105-\beta _{1})q^{2}+(-7198+2\beta _{1}+\cdots)q^{3}+\cdots\)
25.22.a.e	$25$	$22$	25.a	1.a	$1$	$7$	$7$	$69.869$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(737\)	\(50381\)	\(0\)	\(817782442\)		$-$	$-$	$2^{13}\cdot 3^{3}\cdot 5^{10}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(105+\beta _{1})q^{2}+(7198-2\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
25.22.a.f	$25$	$22$	25.a	1.a	$1$	$10$	$10$	$69.869$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$2^{30}\cdot 3^{10}\cdot 5^{24}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(6\beta _{1}-\beta _{4})q^{3}+(927372+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)