[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
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
\( p \)
Sign
\(3\)
\(1\)
\(5\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} + 803T_{2}^{2} - 6180860T_{2} - 4487879424 \)
T2^3 + 803*T2^2 - 6180860*T2 - 4487879424
acting on \(S_{22}^{\mathrm{new}}(\Gamma_0(75))\).
$p$
$F_p(T)$
$2$
\( T^{3} + 803 T^{2} + \cdots - 4487879424 \)
T^3 + 803*T^2 - 6180860*T - 4487879424
$3$
\( (T + 59049)^{3} \)
(T + 59049)^3
$5$
\( T^{3} \)
T^3
$7$
\( T^{3} - 1577598316 T^{2} + \cdots + 38\!\cdots\!80 \)
T^3 - 1577598316*T^2 - 80277147740650896*T + 384302090775086165461106880
$11$
\( T^{3} - 84497282000 T^{2} + \cdots + 25\!\cdots\!36 \)
T^3 - 84497282000*T^2 + 1184706006195089475328*T + 25382659565471421049126608654336
$13$
\( T^{3} + 1065489966310 T^{2} + \cdots + 10\!\cdots\!28 \)
T^3 + 1065489966310*T^2 + 222580271976944495787212*T + 10393784694758219869013086733099528
$17$
\( T^{3} + 13851876239906 T^{2} + \cdots - 16\!\cdots\!92 \)
T^3 + 13851876239906*T^2 + 45461221388097954158159212*T - 16612003948581798441604497076324281192
$19$
\( T^{3} - 26858848298644 T^{2} + \cdots + 39\!\cdots\!00 \)
T^3 - 26858848298644*T^2 - 1987786606833494272954737040*T + 39901138453155897129668380348372218990400
$23$
\( T^{3} + 75776598293952 T^{2} + \cdots - 12\!\cdots\!80 \)
T^3 + 75776598293952*T^2 - 1547146044002110380744717504*T - 126406343062727436032852909213591117614080
$29$
\( T^{3} + 911172744177122 T^{2} + \cdots - 19\!\cdots\!00 \)
T^3 + 911172744177122*T^2 - 11868978117076478439732191098580*T - 19398296238205585670151695472729905658859367400
$31$
\( T^{3} + \cdots + 10\!\cdots\!00 \)
T^3 + 14770635893644696*T^2 + 68764729601715575359093490363904*T + 102143443910561919349818780846687689972315289600
$37$
\( T^{3} + \cdots + 18\!\cdots\!60 \)
T^3 - 33876604648537146*T^2 + 66422738480466174489741973265484*T + 1856516021914410841378980803270754741948217863560
$41$
\( T^{3} + \cdots - 86\!\cdots\!00 \)
T^3 - 4403226550677934*T^2 - 22406680737261161340903543090028436*T - 867629622049032832503812213909224937102536608604200
$43$
\( T^{3} + \cdots + 19\!\cdots\!04 \)
T^3 - 76568115811359884*T^2 - 30090837580428454619603501969787856*T + 1993567889494200619122396877774228352740836339283904
$47$
\( T^{3} + \cdots - 62\!\cdots\!68 \)
T^3 + 178877159689418912*T^2 - 244203971226571631038444540453532864*T - 62399158355151406494885821281995593199182934797626368
$53$
\( T^{3} + \cdots - 96\!\cdots\!40 \)
T^3 + 4013622553495571102*T^2 + 3527410919034545607871955969197525036*T - 960481637140812271971363153924292909847030125822242840
$59$
\( T^{3} + \cdots - 67\!\cdots\!00 \)
T^3 + 4476302860362619024*T^2 - 22237311648679359872473191162890297600*T - 67867588839409562001488792797567705863500115303096422400
$61$
\( T^{3} + \cdots - 41\!\cdots\!32 \)
T^3 - 13672812736400197042*T^2 + 51025086813933687178649924931669980396*T - 41782042933101050295381786780619291814630325857299673432
$67$
\( T^{3} + \cdots + 29\!\cdots\!48 \)
T^3 + 10024292550718281716*T^2 - 217905959426166583346183435037320196048*T + 299411770712276310693946451762078522364251328432909402048
$71$
\( T^{3} + \cdots + 14\!\cdots\!52 \)
T^3 - 31548512648354310016*T^2 - 860730498233554822885095751791633563648*T + 14100675384073511476596050313114519258833651575940922212352
$73$
\( T^{3} + \cdots + 10\!\cdots\!20 \)
T^3 + 80637656440064589382*T^2 + 1877249741475985938333216679667178520076*T + 10283753374443955391855754199876700493362344980469355373320
$79$
\( T^{3} + \cdots - 61\!\cdots\!00 \)
T^3 + 101660087769974505880*T^2 - 6020709339121699219102465408820611468800*T - 610599291533098928137426062955631445296079770685298406400000
$83$
\( T^{3} + \cdots + 10\!\cdots\!92 \)
T^3 - 98643502167172343676*T^2 - 36747788653975913720417914117403949902160*T + 1014684054740351801021732333324392602110238949659347803622592
$89$
\( T^{3} + \cdots + 26\!\cdots\!00 \)
T^3 - 49757751372279077814*T^2 - 185603716710655429965708514465185542674740*T + 26441076121183417860573768341306657509893398346026447252595000
$97$
\( T^{3} + \cdots - 16\!\cdots\!52 \)
T^3 + 767965200855128324166*T^2 - 1950359243087223391777049296912734771490548*T - 1636463328080449935350370071382319195159767421523671993718357752
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