[N,k,chi] = [1280,3,Mod(1151,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.1151");
S:= CuspForms(chi, 3);
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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\)
\(257\)
\(261\)
\(511\)
\(\chi(n)\)
\(1\)
\(-1\)
\(-1\)
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
\( T_{3}^{8} + 8T_{3}^{7} - 16T_{3}^{6} - 240T_{3}^{5} - 224T_{3}^{4} + 1664T_{3}^{3} + 3008T_{3}^{2} - 768T_{3} - 2304 \)
T3^8 + 8*T3^7 - 16*T3^6 - 240*T3^5 - 224*T3^4 + 1664*T3^3 + 3008*T3^2 - 768*T3 - 2304
acting on \(S_{3}^{\mathrm{new}}(1280, [\chi])\).
$p$
$F_p(T)$
$2$
\( T^{16} \)
T^16
$3$
\( (T^{8} + 8 T^{7} - 16 T^{6} - 240 T^{5} + \cdots - 2304)^{2} \)
(T^8 + 8*T^7 - 16*T^6 - 240*T^5 - 224*T^4 + 1664*T^3 + 3008*T^2 - 768*T - 2304)^2
$5$
\( (T^{2} + 5)^{8} \)
(T^2 + 5)^8
$7$
\( T^{16} + 480 T^{14} + \cdots + 2932258963456 \)
T^16 + 480*T^14 + 90176*T^12 + 8477568*T^10 + 426748416*T^8 + 11635789824*T^6 + 166747983872*T^4 + 1142395404288*T^2 + 2932258963456
$11$
\( (T^{8} + 32 T^{7} - 16 T^{6} + \cdots - 2569984)^{2} \)
(T^8 + 32*T^7 - 16*T^6 - 7680*T^5 - 37920*T^4 + 299520*T^3 + 865024*T^2 - 1036288*T - 2569984)^2
$13$
\( T^{16} + 1760 T^{14} + \cdots + 11\!\cdots\!96 \)
T^16 + 1760*T^14 + 1245376*T^12 + 453745152*T^10 + 90151466496*T^8 + 9449984434176*T^6 + 452766475927552*T^4 + 6091368349171712*T^2 + 11087598043856896
$17$
\( (T^{8} - 1392 T^{6} - 1024 T^{5} + \cdots - 482211584)^{2} \)
(T^8 - 1392*T^6 - 1024*T^5 + 558048*T^4 - 1089536*T^3 - 72448768*T^2 + 415809536*T - 482211584)^2
$19$
\( (T^{8} + 48 T^{7} - 624 T^{6} + \cdots + 1870799104)^{2} \)
(T^8 + 48*T^7 - 624*T^6 - 56512*T^5 - 419232*T^4 + 13314304*T^3 + 232007936*T^2 + 1222605824*T + 1870799104)^2
$23$
\( T^{16} + 4576 T^{14} + \cdots + 48\!\cdots\!16 \)
T^16 + 4576*T^14 + 8264000*T^12 + 7545781120*T^10 + 3698447354368*T^8 + 947212886200320*T^6 + 113497038826721280*T^4 + 5204169304140054528*T^2 + 48869661445644681216
$29$
\( T^{16} + 6944 T^{14} + \cdots + 56\!\cdots\!36 \)
T^16 + 6944*T^14 + 17835456*T^12 + 22484876800*T^10 + 15371097703936*T^8 + 5894409721864192*T^6 + 1249097088292995072*T^4 + 134392624323794960384*T^2 + 5638140503797530689536
$31$
\( T^{16} + 4352 T^{14} + \cdots + 53\!\cdots\!36 \)
T^16 + 4352*T^14 + 6579200*T^12 + 4610416640*T^10 + 1707937497088*T^8 + 351134023680000*T^6 + 39769169901649920*T^4 + 2311567986407768064*T^2 + 53759721850049396736
$37$
\( T^{16} + 13856 T^{14} + \cdots + 11\!\cdots\!36 \)
T^16 + 13856*T^14 + 74218944*T^12 + 196260974080*T^10 + 268355311339008*T^8 + 178751641164898304*T^6 + 47619995870783979520*T^4 + 4075760511956568637440*T^2 + 11875280424332165185536
$41$
\( (T^{8} - 48 T^{7} + \cdots - 966341086976)^{2} \)
(T^8 - 48*T^7 - 6672*T^6 + 315968*T^5 + 11957088*T^4 - 551115008*T^3 - 5768362240*T^2 + 277328841728*T - 966341086976)^2
$43$
\( (T^{8} - 88 T^{7} + \cdots + 200274921216)^{2} \)
(T^8 - 88*T^7 - 3888*T^6 + 554224*T^5 - 11277600*T^4 - 276711808*T^3 + 10694664640*T^2 - 86043879168*T + 200274921216)^2
$47$
\( T^{16} + 15008 T^{14} + \cdots + 80\!\cdots\!16 \)
T^16 + 15008*T^14 + 86245824*T^12 + 243176014720*T^10 + 359933616646656*T^8 + 278247565671133184*T^6 + 105016787069492973568*T^4 + 17055429016383618711552*T^2 + 806302641428007857750016
$53$
\( T^{16} + 15072 T^{14} + \cdots + 94\!\cdots\!76 \)
T^16 + 15072*T^14 + 81220800*T^12 + 193459517952*T^10 + 207413930489344*T^8 + 87534052239679488*T^6 + 12179132174037073920*T^4 + 229715633094883934208*T^2 + 947703185996529074176
$59$
\( (T^{8} - 16 T^{7} + \cdots + 2914995568896)^{2} \)
(T^8 - 16*T^7 - 13424*T^6 + 266560*T^5 + 48035936*T^4 - 978995968*T^3 - 35155994368*T^2 + 516296162304*T + 2914995568896)^2
$61$
\( T^{16} + 20768 T^{14} + \cdots + 59\!\cdots\!96 \)
T^16 + 20768*T^14 + 160014784*T^12 + 583706918400*T^10 + 1086002706433536*T^8 + 1061661327741149184*T^6 + 525010211467202510848*T^4 + 112115894287254772908032*T^2 + 5967678742842548850589696
$67$
\( (T^{8} - 280 T^{7} + \cdots + 196984704870144)^{2} \)
(T^8 - 280*T^7 + 12560*T^6 + 3418160*T^5 - 481780256*T^4 + 22947945600*T^3 - 285883728960*T^2 - 8475741285120*T + 196984704870144)^2
$71$
\( T^{16} + 29056 T^{14} + \cdots + 18\!\cdots\!76 \)
T^16 + 29056*T^14 + 325067776*T^12 + 1789427507200*T^10 + 5116689730109440*T^8 + 7208249151308431360*T^6 + 3929415004470951018496*T^4 + 82388321124438092283904*T^2 + 181764503130417896882176
$73$
\( (T^{8} - 160 T^{7} + \cdots - 1312077678336)^{2} \)
(T^8 - 160*T^7 - 1072*T^6 + 905088*T^5 - 17334048*T^4 - 996761088*T^3 + 14672666880*T^2 + 257126344704*T - 1312077678336)^2
$79$
\( T^{16} + 53248 T^{14} + \cdots + 15\!\cdots\!96 \)
T^16 + 53248*T^14 + 994590720*T^12 + 8238010990592*T^10 + 34904154832896000*T^8 + 80629792025608192000*T^6 + 101409737572984551374848*T^4 + 63895114823356910892220416*T^2 + 15209792973377222038410756096
$83$
\( (T^{8} + 24 T^{7} + \cdots - 6286784368896)^{2} \)
(T^8 + 24*T^7 - 13200*T^6 - 10032*T^5 + 51359520*T^4 - 628281984*T^3 - 59946933824*T^2 + 1335544411392*T - 6286784368896)^2
$89$
\( (T^{8} - 48 T^{7} + \cdots - 255121887096576)^{2} \)
(T^8 - 48*T^7 - 36304*T^6 + 1181632*T^5 + 386121568*T^4 - 11211517184*T^3 - 1172009510144*T^2 + 40014792754176*T - 255121887096576)^2
$97$
\( (T^{8} - 224 T^{7} + \cdots + 24\!\cdots\!96)^{2} \)
(T^8 - 224*T^7 - 13424*T^6 + 4379520*T^5 + 101585376*T^4 - 30385521152*T^3 - 766029609728*T^2 + 71166972266496*T + 2403573887396096)^2
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