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

• Label: 25.6.d
• Level: $25$
• Weight: $6$
• Character orbit: 25.d
• Rep. character: $\chi_{25}(6,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
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	52	52	0
Cusp forms	44	44	0
Eisenstein series	8	8	0

Trace form

44 * q - 7 * q^2 - q^3 - 147 * q^4 + 115 * q^5 + 133 * q^6 - 202 * q^7 - 500 * q^8 - 508 * q^9 - 55 * q^10 + 718 * q^11 - 437 * q^12 - 291 * q^13 - 689 * q^14 - 1125 * q^15 + 2609 * q^16 + 718 * q^17 + 8544 * q^18 + 4075 * q^19 + 1095 * q^20 - 2022 * q^21 - 3704 * q^22 - 1211 * q^23 - 19620 * q^24 - 2405 * q^25 - 17882 * q^26 + 9485 * q^27 + 9371 * q^28 + 14245 * q^29 + 14235 * q^30 - 8637 * q^31 + 30678 * q^32 - 21682 * q^33 - 5639 * q^34 - 36235 * q^35 + 31069 * q^36 - 50777 * q^37 + 6525 * q^38 + 7009 * q^39 - 3470 * q^40 + 5558 * q^41 + 19541 * q^42 + 61194 * q^43 + 26876 * q^44 + 76400 * q^45 + 14553 * q^46 - 46662 * q^47 - 150806 * q^48 - 24482 * q^49 - 21335 * q^50 - 121132 * q^51 + 72648 * q^52 - 93141 * q^53 + 18655 * q^54 + 11760 * q^55 + 47370 * q^56 + 292150 * q^57 - 38730 * q^58 + 47640 * q^59 + 26010 * q^60 - 26747 * q^61 - 46744 * q^62 + 78674 * q^63 + 31148 * q^64 - 61320 * q^65 + 45896 * q^66 + 123558 * q^67 + 123886 * q^68 - 117721 * q^69 + 12280 * q^70 + 110788 * q^71 - 586175 * q^72 - 146691 * q^73 - 179364 * q^74 - 108580 * q^75 - 269280 * q^76 - 153084 * q^77 + 405473 * q^78 - 54065 * q^79 - 360820 * q^80 + 277619 * q^81 - 353334 * q^82 - 54791 * q^83 + 374516 * q^84 + 764240 * q^85 - 74697 * q^86 + 229940 * q^87 + 997600 * q^88 + 217000 * q^89 - 21245 * q^90 - 181052 * q^91 + 801448 * q^92 - 380432 * q^93 - 165099 * q^94 - 61205 * q^95 + 925078 * q^96 - 562302 * q^97 - 982324 * q^98 - 680776 * 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.d.a	$25$	$6$	25.d	25.d	$5$	$44$	$11$	$4.010$		None		✓	✓	✓	25.6.d.a	$2$	$0$	\(-7\)	\(-1\)	\(115\)	\(-202\)		$\mathrm{SU}(2)[C_{5}]$