Space of modular forms of level 125, weight 2, and Character 125.d

• Label: 125.2.d
• Level: $125$
• Weight: $2$
• Character orbit: 125.d
• Rep. character: $\chi_{125}(26,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $25$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(25\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(125, [\chi])\).

	Total	New	Old
Modular forms	68	44	24
Cusp forms	28	20	8
Eisenstein series	40	24	16

Trace form

\( 20 q + 2 q^{2} + q^{3} - 15 q^{6} + 2 q^{7} + 5 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(125, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
125.2.d.a	$125$	$2$	125.d	25.d	$5$	$4$	$1$	$0.998$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(2\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
125.2.d.b	$125$	$2$	125.d	25.d	$5$	$16$	$4$	$0.998$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{2}+(\beta _{6}+\beta _{12}+\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(125, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(125, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)