Space of modular forms of level 125, weight 4, and trivial character

• Label: 125.4.a
• Level: $125$
• Weight: $4$
• Character orbit: 125.a
• Rep. character: $\chi_{125}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $50$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	125.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(50\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(125))\).

	Total	New	Old
Modular forms	43	24	19
Cusp forms	33	24	9
Eisenstein series	10	0	10

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
\(+\)	\(14\)
\(-\)	\(10\)

Trace form

\( 24 q + 102 q^{4} - 2 q^{6} + 218 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(125))\) 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
125.4.a.a	$125$	$4$	125.a	1.a	$1$	$4$	$4$	$7.375$	4.4.12400.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots\)
125.4.a.b	$125$	$4$	125.a	1.a	$1$	$6$	$6$	$7.375$	6.6.497918125.1	None	✓	$1$	$1$	\(-7\)	\(-14\)	\(0\)	\(-67\)		$-$	$-$	$5^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{2}+(-2-\beta _{1})q^{3}+(5+\cdots)q^{4}+\cdots\)
125.4.a.c	$125$	$4$	125.a	1.a	$1$	$6$	$6$	$7.375$	6.6.497918125.1	None	✓	$1$	$0$	\(7\)	\(14\)	\(0\)	\(67\)		$+$	$+$	$5^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{2}+(2+\beta _{1})q^{3}+(5-\beta _{2}+\cdots)q^{4}+\cdots\)
125.4.a.d	$125$	$4$	125.a	1.a	$1$	$8$	$8$	$7.375$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$2^{2}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}+\beta _{4}q^{3}+(5-\beta _{3})q^{4}+(5-\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(125))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(125)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)