[N,k,chi] = [72,11,Mod(19,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.19");
S:= CuspForms(chi, 11);
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
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\)
\(37\)
\(55\)
\(65\)
\(\chi(n)\)
\(-1\)
\(-1\)
\(1\)
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 subspace can be constructed as the kernel of the linear operator
\( T_{5}^{8} + 48458880 T_{5}^{6} + 643618525286400 T_{5}^{4} + \cdots + 16\!\cdots\!00 \)
T5^8 + 48458880*T5^6 + 643618525286400*T5^4 + 2340077207246733312000*T5^2 + 1619965775150320252354560000
acting on \(S_{11}^{\mathrm{new}}(72, [\chi])\).
$p$
$F_p(T)$
$2$
\( T^{8} + 42 T^{7} + \cdots + 1099511627776 \)
T^8 + 42*T^7 + 776*T^6 + 7872*T^5 + 537600*T^4 + 8060928*T^3 + 813694976*T^2 + 45097156608*T + 1099511627776
$3$
\( T^{8} \)
T^8
$5$
\( T^{8} + 48458880 T^{6} + \cdots + 16\!\cdots\!00 \)
T^8 + 48458880*T^6 + 643618525286400*T^4 + 2340077207246733312000*T^2 + 1619965775150320252354560000
$7$
\( T^{8} + 1170117120 T^{6} + \cdots + 16\!\cdots\!00 \)
T^8 + 1170117120*T^6 + 418288688194191360*T^4 + 53649351268507396991877120*T^2 + 1640680591178422839524940840960000
$11$
\( (T^{4} + 71664 T^{3} + \cdots + 56\!\cdots\!48)^{2} \)
(T^4 + 71664*T^3 - 51164702888*T^2 - 1465711801033920*T + 561997863000053423248)^2
$13$
\( T^{8} + 643617006720 T^{6} + \cdots + 43\!\cdots\!00 \)
T^8 + 643617006720*T^6 + 142312487606089740718080*T^4 + 13203589907618367280385515223777280*T^2 + 439844617787378856522768990693721032464793600
$17$
\( (T^{4} - 185400 T^{3} + \cdots + 29\!\cdots\!32)^{2} \)
(T^4 - 185400*T^3 - 4072710739304*T^2 + 1195608059520458016*T + 2932182208397474385686032)^2
$19$
\( (T^{4} - 876656 T^{3} + \cdots + 20\!\cdots\!48)^{2} \)
(T^4 - 876656*T^3 - 10780243401768*T^2 + 494846390507012800*T + 20486258675110172393173648)^2
$23$
\( T^{8} + 126385472340480 T^{6} + \cdots + 16\!\cdots\!00 \)
T^8 + 126385472340480*T^6 + 4202655117458274336310886400*T^4 + 48856020108342812713088052148423360512000*T^2 + 161650779349937787542432579085725665993914958479360000
$29$
\( T^{8} + \cdots + 13\!\cdots\!00 \)
T^8 + 3009463277228160*T^6 + 2942761031369077290419253350400*T^4 + 1102435997452805050669893457197623027533086720*T^2 + 134513474602856067043352414577223525403914217515567703654400
$31$
\( T^{8} + \cdots + 43\!\cdots\!00 \)
T^8 + 4319975695196160*T^6 + 6250491661179408192513245184000*T^4 + 3335336855602101662364805090952889149423616000*T^2 + 430550622346803718089293449426312374787427140264148336640000
$37$
\( T^{8} + \cdots + 11\!\cdots\!00 \)
T^8 + 21916995217441920*T^6 + 100994253707183245809473837076480*T^4 + 14209010949320186166830078931977022296445419520*T^2 + 110732364766587041597377626862641298186841810586634184294400
$41$
\( (T^{4} + 46334664 T^{3} + \cdots + 68\!\cdots\!88)^{2} \)
(T^4 + 46334664*T^3 - 14423799522910568*T^2 - 531884097618693290845920*T + 6818172686284910410048187715088)^2
$43$
\( (T^{4} + 5095312 T^{3} + \cdots - 51\!\cdots\!16)^{2} \)
(T^4 + 5095312*T^3 - 8313019522329000*T^2 + 388790660976438162659008*T - 5142584724350036800151726735216)^2
$47$
\( T^{8} + \cdots + 43\!\cdots\!00 \)
T^8 + 286254889253652480*T^6 + 22115078826931391439062446610841600*T^4 + 524238876972406429062061037796146587859751240990720*T^2 + 430682685841797803253523773874777473944885574689294847726688665600
$53$
\( T^{8} + \cdots + 20\!\cdots\!00 \)
T^8 + 453067498196519040*T^6 + 59994488193032748368244865603276800*T^4 + 2470864158905525156233359653465264369908800757432320*T^2 + 206922491667113759986192466983310506045455203472686721984469401600
$59$
\( (T^{4} - 482821008 T^{3} + \cdots + 47\!\cdots\!56)^{2} \)
(T^4 - 482821008*T^3 - 530098260364733096*T^2 - 40723638827990332932472512*T + 4731852285803389052091589311296656)^2
$61$
\( T^{8} + \cdots + 41\!\cdots\!00 \)
T^8 + 3099009183128983680*T^6 + 2184873723657140133430947954683351040*T^4 + 42199507034449488299079385643660623813881122421473280*T^2 + 41322477042047183821620658265788002012531723606328078807826064998400
$67$
\( (T^{4} + 612791440 T^{3} + \cdots - 13\!\cdots\!88)^{2} \)
(T^4 + 612791440*T^3 - 394823457833525544*T^2 - 215848381404121070021093696*T - 13470422952560148088576097403218288)^2
$71$
\( T^{8} + \cdots + 81\!\cdots\!00 \)
T^8 + 8973404139914703360*T^6 + 22424417746190520903519609935441756160*T^4 + 10174941999868072108643810992116039169409553146346209280*T^2 + 818726356558834825638843520654513960689768644425913734359709168277913600
$73$
\( (T^{4} - 1400036360 T^{3} + \cdots + 23\!\cdots\!12)^{2} \)
(T^4 - 1400036360*T^3 - 9139206384684599784*T^2 + 6668151876059385730157672416*T + 23039198536616729474203027791076202512)^2
$79$
\( T^{8} + \cdots + 57\!\cdots\!00 \)
T^8 + 29766050720867174400*T^6 + 268100269388784835983818404325653217280*T^4 + 786460192312842224470773746985042814911458883183071723520*T^2 + 579385089761870906732266833400531052610459835896431089657270314702628454400
$83$
\( (T^{4} + 926711280 T^{3} + \cdots + 77\!\cdots\!72)^{2} \)
(T^4 + 926711280*T^3 - 18671042709998066984*T^2 - 9321901234100877703721539776*T + 77804917618633483521203231108246845072)^2
$89$
\( (T^{4} + 3081298056 T^{3} + \cdots + 20\!\cdots\!28)^{2} \)
(T^4 + 3081298056*T^3 - 47705925257313466088*T^2 + 70496642898631238645720555040*T + 20832556288124978587501394380693773328)^2
$97$
\( (T^{4} + 4848931768 T^{3} + \cdots + 57\!\cdots\!84)^{2} \)
(T^4 + 4848931768*T^3 - 173464819639683191400*T^2 - 37488526770626682271768486688*T + 571758199007907984528136970531396448784)^2
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