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

• Label: 125.2.e
• Level: $125$
• Weight: $2$
• Character orbit: 125.e
• Rep. character: $\chi_{125}(24,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $25$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.e (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(25\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	72	40	32
Cusp forms	32	16	16
Eisenstein series	40	24	16

Trace form

\( 16 q + 5 q^{2} + 5 q^{3} + 3 q^{4} - 3 q^{6} - 10 q^{8} - 3 q^{9} + O(q^{10}) \)

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.e.a	$125$	$2$	125.e	25.e	$10$	$8$	$2$	$0.998$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}-\zeta_{20}q^{3}+\cdots\)
125.2.e.b	$125$	$2$	125.e	25.e	$10$	$8$	$2$	$0.998$	8.0.58140625.2	None		$2$	$0$	\(5\)	\(5\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{7})q^{3}+\cdots\)

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

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