Space of modular forms of level 25, weight 16, and trivial character

• Label: 25.16.a
• Level: $25$
• Weight: $16$
• Character orbit: 25.a
• Rep. character: $\chi_{25}(1,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $6$
• Sturm bound: $40$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(40\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(25))\).

	Total	New	Old
Modular forms	41	25	16
Cusp forms	35	22	13
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
\(+\)	\(11\)
\(-\)	\(11\)

Trace form

\( 22 q + 90 q^{2} - 1910 q^{3} + 379126 q^{4} - 1175286 q^{6} + 1503650 q^{7} + 1059480 q^{8} + 105452364 q^{9} + O(q^{10}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(25))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5
25.16.a.a	$25$	$16$	25.a	1.a	$1$	$1$	$1$	$35.673$	\(\Q\)	None	✓				1.16.a.a	$1$	$0$	\(-216\)	\(3348\)	\(0\)	\(-2822456\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-6^{3}q^{2}+3348q^{3}+13888q^{4}-723168q^{6}+\cdots\)
25.16.a.b	$25$	$16$	25.a	1.a	$1$	$2$	$2$	$35.673$	\(\Q(\sqrt{3169}) \)	None	✓				5.16.a.a	$1$	$0$	\(310\)	\(-1740\)	\(0\)	\(3420900\)		$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(155-\beta )q^{2}+(-870-2\beta )q^{3}+(19778+\cdots)q^{4}+\cdots\)
25.16.a.c	$25$	$16$	25.a	1.a	$1$	$3$	$3$	$35.673$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				5.16.a.b	$1$	$0$	\(-4\)	\(-3518\)	\(0\)	\(905206\)		$+$	$+$	$2^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1170+2^{4}\beta _{1}+\cdots)q^{3}+\cdots\)
25.16.a.d	$25$	$16$	25.a	1.a	$1$	$5$	$5$	$35.673$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			25.16.a.d	$1$	$1$	\(-39\)	\(-7003\)	\(0\)	\(-2718694\)		$-$	$-$	$2^{8}\cdot 3\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(-8+\beta _{1})q^{2}+(-1400-3\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
25.16.a.e	$25$	$16$	25.a	1.a	$1$	$5$	$5$	$35.673$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓		25.16.a.d	$1$	$0$	\(39\)	\(7003\)	\(0\)	\(2718694\)		$+$	$+$	$2^{8}\cdot 3\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(8-\beta _{1})q^{2}+(1400+3\beta _{1}+\beta _{2})q^{3}+\cdots\)
25.16.a.f	$25$	$16$	25.a	1.a	$1$	$6$	$6$	$35.673$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		5.16.b.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$2^{14}\cdot 3^{4}\cdot 5^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(6428+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(25)) \simeq \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)