[N,k,chi] = [5,20,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{4} + 420T_{2}^{3} - 2002872T_{2}^{2} - 746347520T_{2} + 237314973696 \)
T2^4 + 420*T2^3 - 2002872*T2^2 - 746347520*T2 + 237314973696
acting on \(S_{20}^{\mathrm{new}}(\Gamma_0(5))\).
$p$
$F_p(T)$
$2$
\( T^{4} + 420 T^{3} + \cdots + 237314973696 \)
T^4 + 420*T^3 - 2002872*T^2 - 746347520*T + 237314973696
$3$
\( T^{4} - 3080 T^{3} + \cdots + 17\!\cdots\!16 \)
T^4 - 3080*T^3 - 2396812008*T^2 + 7524612119520*T + 177346815108838416
$5$
\( (T + 1953125)^{4} \)
(T + 1953125)^4
$7$
\( T^{4} - 214021400 T^{3} + \cdots - 35\!\cdots\!04 \)
T^4 - 214021400*T^3 - 19986788531781672*T^2 + 6696544649839234487690400*T - 351419826901277279646180629221104
$11$
\( T^{4} - 11585712768 T^{3} + \cdots - 53\!\cdots\!04 \)
T^4 - 11585712768*T^3 - 62616109046686626816*T^2 + 449788474059133193821630824448*T - 531772352902616082812185517662094229504
$13$
\( T^{4} - 14812333160 T^{3} + \cdots + 38\!\cdots\!36 \)
T^4 - 14812333160*T^3 - 2288161007469788162088*T^2 + 22622501054730936411184433855840*T + 385979825126249942646736326402549212043536
$17$
\( T^{4} - 849033742440 T^{3} + \cdots - 65\!\cdots\!04 \)
T^4 - 849033742440*T^3 + 2538322874794380218328*T^2 + 95886956149488698958597000397606240*T - 6580952719913845285908537578798492806319998704
$19$
\( T^{4} - 1978167708560 T^{3} + \cdots + 33\!\cdots\!00 \)
T^4 - 1978167708560*T^3 - 4238025052804808323677600*T^2 + 5955061789332436104442902440649824000*T + 3337592024313946255248202446062254186333918880000
$23$
\( T^{4} + 26569906952760 T^{3} + \cdots - 42\!\cdots\!44 \)
T^4 + 26569906952760*T^3 + 186871139400644875910759832*T^2 - 215229152870856498423967262302277579040*T - 4259451596454867139929668016348369487396106531407344
$29$
\( T^{4} - 116267174339640 T^{3} + \cdots - 13\!\cdots\!00 \)
T^4 - 116267174339640*T^3 - 2314184692649364902325834600*T^2 + 547932737966617876870525003947480775796000*T - 13323409311059970708223200652037516593910946839685270000
$31$
\( T^{4} - 251049672388688 T^{3} + \cdots - 30\!\cdots\!44 \)
T^4 - 251049672388688*T^3 - 36819438954687639061515854496*T^2 + 9436596908690590090230157206785570170430208*T - 304426638223702168395264530281470955806766950215075122944
$37$
\( T^{4} - 53471657716520 T^{3} + \cdots + 35\!\cdots\!96 \)
T^4 - 53471657716520*T^3 - 865236711736384588153931944872*T^2 + 213805993578966491539414179895009644611636320*T + 35364901265744283630721082883920698815286067946457983655696
$41$
\( T^{4} + \cdots + 54\!\cdots\!36 \)
T^4 - 5606221897948248*T^3 + 8406635420922175223356425311064*T^2 - 4337302553679028816033624863598580229824329312*T + 546310494333227996621217480809682275792022085100735607960336
$43$
\( T^{4} + \cdots + 10\!\cdots\!96 \)
T^4 - 3924193112762600*T^3 - 10626191710683454281539080997928*T^2 + 36132019184154951241586010232168060620428866400*T + 10353060934422940012548640709411860549306831127085505692033296
$47$
\( T^{4} + \cdots - 43\!\cdots\!04 \)
T^4 - 9972444326989560*T^3 + 13231357759690109218696631003928*T^2 + 51524094562899123233088583793467309635824918560*T - 43746184114552378790387422271157465858642157468515702183224304
$53$
\( T^{4} + \cdots + 52\!\cdots\!16 \)
T^4 + 7462276270800120*T^3 - 740572146743249408766644267269608*T^2 - 393034180799432400214407402636112537293862069280*T + 52268787312150099238080682411024361850056551132040953403179980816
$59$
\( T^{4} + \cdots + 37\!\cdots\!00 \)
T^4 - 186154941962838480*T^3 + 12549267303631165829064310760565600*T^2 - 361718232041531193192697030091955488241727929632000*T + 3763161011168960451792438727345610741788820028632562064236600480000
$61$
\( T^{4} + \cdots + 59\!\cdots\!96 \)
T^4 - 248517593110644968*T^3 + 19535815107903113620465056749895384*T^2 - 598576575686218081221026414179722088553123570337952*T + 5901641525512680730602650311222464717650104116113543286898200014096
$67$
\( T^{4} + \cdots + 53\!\cdots\!96 \)
T^4 + 83976946080676360*T^3 - 73482052969568566768017090607101672*T^2 - 5884396824548145497680824384296244009107624038126560*T + 53404996524844442613254387614010938676035981283938374700388590945296
$71$
\( T^{4} + \cdots + 10\!\cdots\!76 \)
T^4 + 326854508200029072*T^3 - 332517187498832856155859002899057056*T^2 - 17602016341668332908431185549044204130717554481788672*T + 10665238894467820487638948549186057067175928647682072006129597597982976
$73$
\( T^{4} + \cdots - 98\!\cdots\!44 \)
T^4 - 706071038062266440*T^3 + 18884761538909418840944755236571032*T^2 + 63031128198843582855603929141823561989960123681473760*T - 9822191240660460019634925573495707455978405396082640762454714448668144
$79$
\( T^{4} + \cdots - 10\!\cdots\!00 \)
T^4 - 1300235890504742240*T^3 - 2433007653020188978280272332600105600*T^2 + 3627522701380411017917746560325815329127050625536256000*T - 1003319672445572836074915326286933838623165541515793043514117954270720000
$83$
\( T^{4} + \cdots - 18\!\cdots\!24 \)
T^4 + 894716269324765080*T^3 - 3103493950978632732485680712748094248*T^2 - 4854921096877938757003757161822535199895717865951106720*T - 1858391851226848257684751544745962786327028494684057461651928538557674224
$89$
\( T^{4} + \cdots - 22\!\cdots\!00 \)
T^4 + 4392730519471649880*T^3 - 25448003918907596738034382614046559400*T^2 - 84068842062061756772176523403533868090486863810452548000*T - 2272706295755305180471189770233311590886127019914869781271972010391670000
$97$
\( T^{4} + \cdots + 27\!\cdots\!96 \)
T^4 - 1437870497951780360*T^3 - 16410933956484117092529951203679722472*T^2 - 5009367278880108880315891445008084686090903518781892640*T + 27341018487071127477941661793478534869826514265942017525166606434137518096
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