[N,k,chi] = [230,6,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.1");
S:= CuspForms(chi, 6);
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
\(2\)
\(-1\)
\(5\)
\(1\)
\(23\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{6} - 15T_{3}^{5} - 1066T_{3}^{4} + 9561T_{3}^{3} + 307311T_{3}^{2} - 900468T_{3} - 12520800 \)
T3^6 - 15*T3^5 - 1066*T3^4 + 9561*T3^3 + 307311*T3^2 - 900468*T3 - 12520800
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(230))\).
$p$
$F_p(T)$
$2$
\( (T - 4)^{6} \)
(T - 4)^6
$3$
\( T^{6} - 15 T^{5} - 1066 T^{4} + \cdots - 12520800 \)
T^6 - 15*T^5 - 1066*T^4 + 9561*T^3 + 307311*T^2 - 900468*T - 12520800
$5$
\( (T + 25)^{6} \)
(T + 25)^6
$7$
\( T^{6} - 106 T^{5} + \cdots + 165428983104 \)
T^6 - 106*T^5 - 47804*T^4 + 4322851*T^3 + 217369064*T^2 - 18748948820*T + 165428983104
$11$
\( T^{6} + \cdots - 221236397079552 \)
T^6 - 321*T^5 - 292689*T^4 + 40641750*T^3 + 28636746048*T^2 + 1314020686896*T - 221236397079552
$13$
\( T^{6} - 527 T^{5} + \cdots + 66\!\cdots\!16 \)
T^6 - 527*T^5 - 1347474*T^4 + 794899305*T^3 + 121409606835*T^2 - 75466026870480*T + 6606225862820316
$17$
\( T^{6} + 660 T^{5} + \cdots - 22\!\cdots\!80 \)
T^6 + 660*T^5 - 8384902*T^4 - 7133346883*T^3 + 17999095696326*T^2 + 17454762350043760*T - 2240582438923781280
$19$
\( T^{6} - 2749 T^{5} + \cdots + 29\!\cdots\!28 \)
T^6 - 2749*T^5 - 6968603*T^4 + 23645030182*T^3 + 3758647852400*T^2 - 49151645113971152*T + 29724256493958812928
$23$
\( (T + 529)^{6} \)
(T + 529)^6
$29$
\( T^{6} - 3337 T^{5} + \cdots - 13\!\cdots\!32 \)
T^6 - 3337*T^5 - 87036309*T^4 + 251950573481*T^3 + 2217505556969140*T^2 - 4793561882935386456*T - 13926442782715304168232
$31$
\( T^{6} - 31094 T^{5} + \cdots + 68\!\cdots\!60 \)
T^6 - 31094*T^5 + 338057117*T^4 - 1317255697385*T^3 - 514138920749626*T^2 + 9072856885157236843*T + 6853654106211122156560
$37$
\( T^{6} - 27037 T^{5} + \cdots - 36\!\cdots\!08 \)
T^6 - 27037*T^5 + 121090838*T^4 + 2331531034152*T^3 - 25531366298453072*T^2 + 71573167094015114176*T - 3677485003327778046208
$41$
\( T^{6} - 33608 T^{5} + \cdots + 18\!\cdots\!46 \)
T^6 - 33608*T^5 + 62704443*T^4 + 6593621850535*T^3 - 39294948984849698*T^2 - 265824462624026941119*T + 1825939925800739878715046
$43$
\( T^{6} - 17024 T^{5} + \cdots + 13\!\cdots\!20 \)
T^6 - 17024*T^5 - 355118044*T^4 + 8406828306720*T^3 - 29400205966928384*T^2 - 250956695186288877568*T + 1332094082896692551352320
$47$
\( T^{6} - 16864 T^{5} + \cdots + 29\!\cdots\!00 \)
T^6 - 16864*T^5 - 553869551*T^4 + 11306573830198*T^3 + 4040917609232900*T^2 - 864096090241591919360*T + 2968830462706105665196800
$53$
\( T^{6} + 8475 T^{5} + \cdots - 80\!\cdots\!36 \)
T^6 + 8475*T^5 - 1703143386*T^4 - 20094793340616*T^3 + 625064470555621824*T^2 + 4821684754689453157488*T - 80728772002066947724357536
$59$
\( T^{6} - 7899 T^{5} + \cdots - 29\!\cdots\!88 \)
T^6 - 7899*T^5 - 2529430030*T^4 + 2938893533204*T^3 + 1762685487550225584*T^2 + 3984527725385925978112*T - 296178982428725422665189888
$61$
\( T^{6} - 25437 T^{5} + \cdots + 57\!\cdots\!92 \)
T^6 - 25437*T^5 - 2530002649*T^4 + 46393894255178*T^3 + 1142353925192735088*T^2 - 21986863696978133845232*T + 57345112266569124315259392
$67$
\( T^{6} + 25517 T^{5} + \cdots + 13\!\cdots\!20 \)
T^6 + 25517*T^5 - 4371029228*T^4 - 39250915635288*T^3 + 3888015748633695168*T^2 + 14466956473216040828544*T + 13221325259798435938897920
$71$
\( T^{6} - 17204 T^{5} + \cdots - 31\!\cdots\!80 \)
T^6 - 17204*T^5 - 10703341295*T^4 + 104701875710777*T^3 + 34803123027317476358*T^2 - 116235770470335851851549*T - 31835220711077762241411376080
$73$
\( T^{6} - 760 T^{5} + \cdots + 72\!\cdots\!48 \)
T^6 - 760*T^5 - 2197845799*T^4 + 30838423107594*T^3 + 330926548507971016*T^2 - 4649547462161869006760*T + 721885663962396883272848
$79$
\( T^{6} - 66972 T^{5} + \cdots + 93\!\cdots\!56 \)
T^6 - 66972*T^5 - 7425921544*T^4 + 493768556639040*T^3 + 9439683733291161600*T^2 - 801507885231193911221760*T + 9317426502635158069467795456
$83$
\( T^{6} - 58523 T^{5} + \cdots + 62\!\cdots\!04 \)
T^6 - 58523*T^5 - 14376428924*T^4 + 1013570434626332*T^3 + 27663368410864357664*T^2 - 3311669613255102226148224*T + 62094260261458345360846485504
$89$
\( T^{6} - 38406 T^{5} + \cdots + 77\!\cdots\!48 \)
T^6 - 38406*T^5 - 17764458804*T^4 - 37873901031480*T^3 + 74495494486893530592*T^2 + 2323521219990180847131648*T + 7726909069862252757478914048
$97$
\( T^{6} - 82861 T^{5} + \cdots + 27\!\cdots\!76 \)
T^6 - 82861*T^5 - 30340704599*T^4 + 2628743862316612*T^3 + 176346220455113912408*T^2 - 18526042421191330439508512*T + 275709599816824450805782847376
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