Space of modular forms of level 25, weight 12, and trivial character

• Label: 25.12.a
• Level: $25$
• Weight: $12$
• Character orbit: 25.a
• Rep. character: $\chi_{25}(1,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $6$
• Sturm bound: $30$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(30\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(25))\).

	Total	New	Old
Modular forms	31	19	12
Cusp forms	25	16	9
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
\(+\)	\(8\)
\(-\)	\(8\)

Trace form

\( 16 q + 10 q^{2} + 760 q^{3} + 15798 q^{4} - 36918 q^{6} - 23600 q^{7} + 261720 q^{8} + 688512 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.12.a.a	$25$	$12$	25.a	1.a	$1$	$1$	$1$	$19.209$	\(\Q\)	None	✓	$1$	$0$	\(-34\)	\(792\)	\(0\)	\(17556\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-34q^{2}+792q^{3}-892q^{4}-26928q^{6}+\cdots\)
25.12.a.b	$25$	$12$	25.a	1.a	$1$	$1$	$1$	$19.209$	\(\Q\)	None	✓	$1$	$0$	\(24\)	\(-252\)	\(0\)	\(16744\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+24q^{2}-252q^{3}-1472q^{4}-6048q^{6}+\cdots\)
25.12.a.c	$25$	$12$	25.a	1.a	$1$	$2$	$2$	$19.209$	\(\Q(\sqrt{151}) \)	None	✓	$1$	$0$	\(20\)	\(220\)	\(0\)	\(-57900\)		$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(10+3\beta )q^{2}+(110+2^{4}\beta )q^{3}+(3488+\cdots)q^{4}+\cdots\)
25.12.a.d	$25$	$12$	25.a	1.a	$1$	$4$	$4$	$19.209$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(-55\)	\(20\)	\(0\)	\(-96400\)		$-$	$-$	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-14+\beta _{1})q^{2}+(5-2\beta _{1}-\beta _{2})q^{3}+\cdots\)
25.12.a.e	$25$	$12$	25.a	1.a	$1$	$4$	$4$	$19.209$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(18-\beta _{3})q^{4}+(-438+\cdots)q^{6}+\cdots\)
25.12.a.f	$25$	$12$	25.a	1.a	$1$	$4$	$4$	$19.209$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(55\)	\(-20\)	\(0\)	\(96400\)		$+$	$+$	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(14-\beta _{1})q^{2}+(-5+2\beta _{1}+\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)