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

• Label: 125.2.g
• Level: $125$
• Weight: $2$
• Character orbit: 125.g
• Rep. character: $\chi_{125}(6,\cdot)$
• Character field: $\Q(\zeta_{25})$
• Dimension: $220$
• Newform subspaces: $1$
• Sturm bound: $25$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 125 \)
Character field:			\(\Q(\zeta_{25})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(25\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	260	260	0
Cusp forms	220	220	0
Eisenstein series	40	40	0

Trace form

220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * 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.g.a	$125$	$2$	125.g	125.g	$25$	$220$	$11$	$0.998$		None		✓	✓	✓	125.2.g.a	$2$	$0$	\(-20\)	\(-20\)	\(-15\)	\(-15\)		$\mathrm{SU}(2)[C_{25}]$