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Properties

Label 25.34
Level 25
Weight 34
Dimension 751
Nonzero newspaces 4
Sturm bound 1700
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1700\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(25))\).

Total New Old
Modular forms 839 772 67
Cusp forms 811 751 60
Eisenstein series 28 21 7

Trace form

\( 751 q + 9386 q^{2} - 136810022 q^{3} + 40422037758 q^{4} + 260641806145 q^{5} - 31298432844338 q^{6} + 294136698079706 q^{7} + 2005390247652710 q^{8} + 22847016866584482 q^{9} + O(q^{10}) \) \( 751 q + 9386 q^{2} - 136810022 q^{3} + 40422037758 q^{4} + 260641806145 q^{5} - 31298432844338 q^{6} + 294136698079706 q^{7} + 2005390247652710 q^{8} + 22847016866584482 q^{9} - 31105565878668880 q^{10} - 567482817166503738 q^{11} - 3737649552777203754 q^{12} + 6956620406504126278 q^{13} + 58141331135938551686 q^{14} - 4479931753921621200 q^{15} - 1098971616220231698034 q^{16} + 1004033287965344742286 q^{17} - 6055400013819784420262 q^{18} + 2887801294137154494270 q^{19} + 17952908382978233491370 q^{20} - 12844345080820242573498 q^{21} - 136968909668130628666778 q^{22} - 85532225239798435619142 q^{23} - 232778842423397389906580 q^{24} + 591656939814523795202935 q^{25} - 156666905796239352636708 q^{26} + 2569176153934771069901530 q^{27} - 8459132069749372796818378 q^{28} + 5355304529652654775733070 q^{29} - 13214919647262371360236490 q^{30} + 7039363164201636048539102 q^{31} - 77198345549317168095139914 q^{32} + 29019987653261118301933686 q^{33} + 41841645306508897004696606 q^{34} - 18218491234301324028488440 q^{35} - 398121030180797405502878154 q^{36} + 324289399945753041920614321 q^{37} - 1205405847751025506061959060 q^{38} + 1208461053077726497888836054 q^{39} - 3491056339558949169565603060 q^{40} + 572804157559058338899804202 q^{41} - 7573116855891373514757125318 q^{42} + 1625145681120333503653801938 q^{43} - 7622639307177093296231324504 q^{44} + 13751431193766503157344668745 q^{45} - 4199341802787259191038581718 q^{46} - 11182525999674291892282757774 q^{47} + 12732426302315253435227694228 q^{48} + 46697741984313814591250466363 q^{49} + 5637404719943925759590269250 q^{50} + 94843765224779366995494539472 q^{51} - 30166981527558196257444163964 q^{52} - 56350133801112594687482772967 q^{53} + 497644090566115718695087082960 q^{54} - 414433836728401650989279518290 q^{55} + 748213273190614087500259358290 q^{56} - 1035051116547242472007135379050 q^{57} + 317994132448112988997289304740 q^{58} + 580984437213347531627923649490 q^{59} - 4364965087791841369420827333070 q^{60} - 539478754379337376756006101958 q^{61} + 986455915168630515842742300912 q^{62} - 145122701553792305991448082242 q^{63} + 1922498061098998972415534592728 q^{64} + 20120909046271626211260282095 q^{65} + 3320653516012878920002098551534 q^{66} - 867412091497260385184598022894 q^{67} - 10484602617593614411416639319258 q^{68} + 1117701639433468765609421701894 q^{69} + 10019109537279858657577627032590 q^{70} - 13473333304074121288246625504458 q^{71} + 39345420522421610416375020057480 q^{72} + 37150443382453572531199881717838 q^{73} - 205221704450437523215392055773564 q^{74} + 60567856335424404724693244657860 q^{75} + 69659537538842439886245159244420 q^{76} - 100844113769008800215354695369578 q^{77} - 24310748537867116880562187098184 q^{78} + 207334425133942234885415868539350 q^{79} - 132884348426069002913986744187770 q^{80} - 444136893727929082570123480361514 q^{81} + 770365351828883813368286499655782 q^{82} + 205890774341268192111432234566718 q^{83} - 920573893649511216667470310127194 q^{84} + 758392628753407994953834375096505 q^{85} + 676732276906659409881851246179002 q^{86} + 138026108800489227332372282593370 q^{87} + 438314746901682885916686654120830 q^{88} + 183489527214710210443483033706115 q^{89} + 2122296940557321516947895125067390 q^{90} - 956644729891775942556848850414738 q^{91} - 143202238394849362512036088160094 q^{92} + 3655349981110907624476436451733606 q^{93} + 1142324142662581896784558694412806 q^{94} - 2255792020131494615134741602037190 q^{95} - 2333795606425079458936532604835318 q^{96} + 6146148980758360617768682641076626 q^{97} + 1456895081353935135645634242372502 q^{98} - 14044588644716222297999617808766996 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.34.a \(\chi_{25}(1, \cdot)\) 25.34.a.a 2 1
25.34.a.b 5
25.34.a.c 6
25.34.a.d 11
25.34.a.e 11
25.34.a.f 16
25.34.b \(\chi_{25}(24, \cdot)\) 25.34.b.a 4 1
25.34.b.b 10
25.34.b.c 12
25.34.b.d 22
25.34.d \(\chi_{25}(6, \cdot)\) n/a 324 4
25.34.e \(\chi_{25}(4, \cdot)\) n/a 328 4

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

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)