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 - 10 * q^11 - 3 * q^12 - 9 * q^13 - 25 * q^14 - 8 * q^17 - 4 * q^18 + 5 * q^19 - 10 * q^21 + 14 * q^22 + 11 * q^23 + 40 * q^24 - 5 * q^27 - q^28 + 15 * q^29 - 15 * q^31 - 18 * q^32 - 8 * q^33 - 20 * q^34 + 40 * q^36 + 7 * q^37 - 5 * q^38 + 15 * q^39 - q^42 + 6 * q^43 + 10 * q^44 - 25 * q^46 + 2 * q^47 + 6 * q^48 - 50 * q^49 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 5 * q^54 + 20 * q^56 + 10 * q^57 + 10 * q^58 - 5 * q^61 - 6 * q^62 + 6 * q^63 - 5 * q^64 + 30 * q^66 + 2 * q^67 + 4 * q^68 - 35 * q^69 + 20 * q^71 - 10 * q^72 - 9 * q^73 + 30 * q^74 - 20 * q^76 + 4 * q^77 - 3 * q^78 - 15 * q^79 + 55 * q^81 + 4 * q^82 - 9 * q^83 - 40 * q^84 - 15 * q^86 + 10 * q^88 + 30 * q^89 + 12 * q^92 + 12 * q^93 + 55 * q^94 + 30 * q^96 - 8 * q^97 - 11 * q^98 + 40 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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					25.2.d.a	$2$	$0$	\(2\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
125.2.d.b	$125$	$2$	125.d	25.d	$5$	$16$	$4$	$0.998$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None			✓		25.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{2}+(\beta _{6}+\beta _{12}+\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots\)

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

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