Space of modular forms of level 25 and weight 26

• Label: 25.26
• Level: 25
• Weight: 26
• Dimension: 566
• Nonzero newspaces: 4
• Sturm bound: 1300
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 25 = 5^{2} \)
Weight:	\( k \)	=	\( 26 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(1300\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(25))\).

	Total	New	Old
Modular forms	639	587	52
Cusp forms	611	566	45
Eisenstein series	28	21	7

Trace form

566 * q + 8138 * q^2 + 932194 * q^3 + 67111166 * q^4 - 51693845 * q^5 - 24674084018 * q^6 - 130328049202 * q^7 + 192500599910 * q^8 + 5592654983229 * q^9 - 3201442653520 * q^10 + 32495626235442 * q^11 + 117136828552278 * q^12 - 195597190598896 * q^13 + 2458093633836422 * q^14 - 936222642087030 * q^15 - 12760157072304754 * q^16 - 8895477339414542 * q^17 - 29266144282380806 * q^18 + 39120718223528190 * q^19 - 69075468040748950 * q^20 + 68186768462358522 * q^21 - 272466703831897754 * q^22 + 15665846426348394 * q^23 + 312079552755523180 * q^24 + 69958593056852985 * q^25 + 2265159003439735452 * q^26 - 2129103496398925520 * q^27 + 3536184905716775606 * q^28 + 5812373046451448700 * q^29 - 2332498999915384970 * q^30 + 15291399990211138042 * q^31 - 4903817202458395722 * q^32 + 8797169060258508978 * q^33 + 33373594848490779742 * q^34 - 33790308698667880780 * q^35 - 190050562718210385354 * q^36 + 87849895891581376803 * q^37 + 331440477164740615340 * q^38 + 121605078757114551798 * q^39 - 430600876335110230260 * q^40 - 45168979594196407208 * q^41 + 53245369835646068026 * q^42 + 349592862684386822194 * q^43 + 550526783300999500072 * q^44 - 28014484473084187585 * q^45 - 1217888828210177212758 * q^46 + 2573586835314857785438 * q^47 + 5192108496341426306964 * q^48 - 6191615131465165075094 * q^49 - 34407687091010357950 * q^50 + 7629542864337149570592 * q^51 - 15564288533428595650812 * q^52 - 26152906164640669214101 * q^53 + 72231417867642899534480 * q^54 + 24947990044437723796330 * q^55 - 22679661562330405093550 * q^56 - 36109271173148544246250 * q^57 + 86072442505319502123940 * q^58 + 83759632844828186273400 * q^59 - 28920292666088018976910 * q^60 - 14991242926215767672608 * q^61 + 102624096938653542112176 * q^62 - 138409719444916170627916 * q^63 + 56171696548109700683736 * q^64 + 167391304727626789416365 * q^65 - 463750573705681990417426 * q^66 - 157283369011865182044422 * q^67 + 1536131691141478984501286 * q^68 - 1130979090173458689207152 * q^69 - 457061943506938531120050 * q^70 + 312621140569179286258142 * q^71 + 1392269239181295496036680 * q^72 + 931048510051825361308924 * q^73 - 937820391733629103632828 * q^74 - 62723639076028656676790 * q^75 - 471639150716066555224700 * q^76 + 1447324283511562172555526 * q^77 - 6019869641365456582742152 * q^78 + 247061761944525634986430 * q^79 + 5456373053354864958771590 * q^80 - 2894918258399968459475619 * q^81 - 11902953699356931779292634 * q^82 - 8206025749802578272187836 * q^83 + 21676777167748990200983462 * q^84 + 20400240068471059231522765 * q^85 - 23793836797633606511107398 * q^86 - 27427901750224899592502980 * q^87 + 55703756256393167489109630 * q^88 + 17206380919118596117862655 * q^89 - 68650885694305186591309890 * q^90 - 13502663006098059926087398 * q^91 - 20544912214971005702928222 * q^92 + 39450969669603405728994868 * q^93 - 21985678712045579801944058 * q^94 - 4970478485607886799603990 * q^95 - 72551051921532223104541558 * q^96 - 2140426033584817039139712 * q^97 + 58884937996329263252720566 * q^98 + 18380437224070892708978088 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(25))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
25.26.a	\(\chi_{25}(1, \cdot)\)	25.26.a.a	1	1
		25.26.a.b	4
		25.26.a.c	5
		25.26.a.d	8
		25.26.a.e	8
		25.26.a.f	12
25.26.b	\(\chi_{25}(24, \cdot)\)	25.26.b.a	2	1
		25.26.b.b	8
		25.26.b.c	10
		25.26.b.d	16
25.26.d	\(\chi_{25}(6, \cdot)\)	n/a	244	4
25.26.e	\(\chi_{25}(4, \cdot)\)	n/a	248	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)