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Properties

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

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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

\( 566 q + 8138 q^{2} + 932194 q^{3} + 67111166 q^{4} - 51693845 q^{5} - 24674084018 q^{6} - 130328049202 q^{7} + 192500599910 q^{8} + 5592654983229 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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