Space of modular forms of level 25, weight 6, and Character 25.e

• Label: 25.6.e
• Level: $25$
• Weight: $6$
• Character orbit: 25.e
• Rep. character: $\chi_{25}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(25, [\chi])\).

	Total	New	Old
Modular forms	56	56	0
Cusp forms	48	48	0
Eisenstein series	8	8	0

Trace form

48 * q - 5 * q^2 - 5 * q^3 + 189 * q^4 - 60 * q^5 - 139 * q^6 + 610 * q^8 + 1031 * q^9 + 435 * q^10 - 724 * q^11 + 315 * q^12 - 5 * q^13 - 497 * q^14 - 105 * q^15 - 6967 * q^16 - 960 * q^17 + 4075 * q^19 + 9155 * q^20 + 2016 * q^21 - 5450 * q^22 - 10995 * q^23 - 20720 * q^24 - 16610 * q^25 + 21666 * q^26 - 13805 * q^27 + 14235 * q^28 + 17195 * q^29 + 39595 * q^30 + 8631 * q^31 + 28460 * q^33 - 24067 * q^34 - 4145 * q^35 - 43827 * q^36 + 19980 * q^37 - 77385 * q^38 + 6037 * q^39 + 93210 * q^40 - 26514 * q^41 + 182885 * q^42 + 26748 * q^44 - 94185 * q^45 - 14559 * q^46 - 7700 * q^47 - 127830 * q^48 - 130126 * q^49 - 231115 * q^50 + 121116 * q^51 - 189260 * q^52 + 45840 * q^53 + 19985 * q^54 + 79370 * q^55 - 43280 * q^56 + 337370 * q^58 + 47640 * q^59 + 71480 * q^60 + 7791 * q^61 + 135320 * q^62 - 35790 * q^63 + 68204 * q^64 + 197485 * q^65 - 14798 * q^66 - 66180 * q^67 + 17957 * q^69 - 129930 * q^70 - 46694 * q^71 - 50545 * q^72 - 18985 * q^73 - 183292 * q^74 - 202210 * q^75 + 273360 * q^76 - 132990 * q^77 - 665225 * q^78 - 54065 * q^79 + 362810 * q^80 - 382452 * q^81 + 161155 * q^83 + 474258 * q^84 - 83075 * q^85 + 74691 * q^86 + 897680 * q^87 + 578430 * q^88 + 436475 * q^89 + 775655 * q^90 + 181046 * q^91 - 1412870 * q^92 - 336327 * q^94 - 362785 * q^95 - 766024 * q^96 - 475210 * q^97 - 361660 * q^98 - 451848 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(25, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.6.e.a	$25$	$6$	25.e	25.e	$10$	$48$	$12$	$4.010$		None		✓	✓	✓	25.6.e.a	$2$	$0$	\(-5\)	\(-5\)	\(-60\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$