Space of modular forms of level 25, weight 10, and trivial character

• Label: 25.10.a
• Level: $25$
• Weight: $10$
• Character orbit: 25.a
• Rep. character: $\chi_{25}(1,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $5$
• Sturm bound: $25$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(25\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(25))\).

	Total	New	Old
Modular forms	25	16	9
Cusp forms	19	13	6
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
\(+\)	\(6\)
\(-\)	\(7\)

Trace form

\( 13 q + 18 q^{2} - 146 q^{3} + 2646 q^{4} + 5226 q^{6} - 5942 q^{7} + 12600 q^{8} + 100659 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.10.a.a	$25$	$10$	25.a	1.a	$1$	$1$	$1$	$12.876$	\(\Q\)	None	✓	$1$	$1$	\(8\)	\(114\)	\(0\)	\(-4242\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+114q^{3}-448q^{4}+912q^{6}+\cdots\)
25.10.a.b	$25$	$10$	25.a	1.a	$1$	$2$	$2$	$12.876$	\(\Q(\sqrt{1009}) \)	None	✓	$1$	$1$	\(10\)	\(-260\)	\(0\)	\(-1700\)		$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(5-\beta )q^{2}+(-130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)
25.10.a.c	$25$	$10$	25.a	1.a	$1$	$3$	$3$	$12.876$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-33\)	\(-89\)	\(0\)	\(-5258\)		$+$	$+$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q+(-11-\beta _{1})q^{2}+(-30-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
25.10.a.d	$25$	$10$	25.a	1.a	$1$	$3$	$3$	$12.876$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(33\)	\(89\)	\(0\)	\(5258\)		$-$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q+(11+\beta _{1})q^{2}+(30+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
25.10.a.e	$25$	$10$	25.a	1.a	$1$	$4$	$4$	$12.876$	4.4.49740556.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(342-\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)