[N,k,chi] = [1449,4,Mod(1,1449)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1449, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1449.1");
S:= CuspForms(chi, 4);
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
\(3\)
\(-1\)
\(7\)
\(-1\)
\(23\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{9} - 57T_{2}^{7} - 13T_{2}^{6} + 1042T_{2}^{5} + 331T_{2}^{4} - 6570T_{2}^{3} - 1782T_{2}^{2} + 9424T_{2} + 5112 \)
T2^9 - 57*T2^7 - 13*T2^6 + 1042*T2^5 + 331*T2^4 - 6570*T2^3 - 1782*T2^2 + 9424*T2 + 5112
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1449))\).
$p$
$F_p(T)$
$2$
\( T^{9} - 57 T^{7} - 13 T^{6} + \cdots + 5112 \)
T^9 - 57*T^7 - 13*T^6 + 1042*T^5 + 331*T^4 - 6570*T^3 - 1782*T^2 + 9424*T + 5112
$3$
\( T^{9} \)
T^9
$5$
\( T^{9} + 29 T^{8} + \cdots - 2232500544 \)
T^9 + 29*T^8 - 361*T^7 - 15771*T^6 - 11867*T^5 + 2577931*T^4 + 13502080*T^3 - 113810420*T^2 - 1066270464*T - 2232500544
$7$
\( (T - 7)^{9} \)
(T - 7)^9
$11$
\( T^{9} + 12 T^{8} + \cdots + 592551340800 \)
T^9 + 12*T^8 - 5915*T^7 - 69532*T^6 + 9605259*T^5 + 124650124*T^4 - 3846969681*T^3 - 76233566172*T^2 - 291237153344*T + 592551340800
$13$
\( T^{9} + \cdots + 102208163239392 \)
T^9 - 199*T^8 + 6621*T^7 + 1049821*T^6 - 85165985*T^5 + 687175055*T^4 + 104464415126*T^3 - 2666866408884*T^2 + 1415196776344*T + 102208163239392
$17$
\( T^{9} + 116 T^{8} + \cdots + 33\!\cdots\!96 \)
T^9 + 116*T^8 - 28556*T^7 - 3010146*T^6 + 244374499*T^5 + 18660745254*T^4 - 883792641296*T^3 - 22799255057216*T^2 + 549927659150336*T + 3364486882308096
$19$
\( T^{9} - 260 T^{8} + \cdots + 12\!\cdots\!44 \)
T^9 - 260*T^8 - 8269*T^7 + 6899610*T^6 - 374075257*T^5 - 35902981368*T^4 + 3278527161125*T^3 + 4575829094210*T^2 - 6038844380526304*T + 128779376679536544
$23$
\( (T + 23)^{9} \)
(T + 23)^9
$29$
\( T^{9} - 107 T^{8} + \cdots - 91\!\cdots\!12 \)
T^9 - 107*T^8 - 93878*T^7 + 8172918*T^6 + 3040622377*T^5 - 212985559387*T^4 - 41212350112132*T^3 + 2325550700107088*T^2 + 200158209574369536*T - 9141935405993578512
$31$
\( T^{9} - 440 T^{8} + \cdots + 96\!\cdots\!36 \)
T^9 - 440*T^8 - 58726*T^7 + 35697472*T^6 + 763699525*T^5 - 832599448576*T^4 + 13718007545352*T^3 + 6017869473014272*T^2 - 245316744410526832*T + 967359276832366336
$37$
\( T^{9} - 563 T^{8} + \cdots - 23\!\cdots\!04 \)
T^9 - 563*T^8 - 77630*T^7 + 81566614*T^6 - 2226328103*T^5 - 3776217771955*T^4 + 238087056673972*T^3 + 62143525858772496*T^2 - 3384291110681821408*T - 233515112294662601104
$41$
\( T^{9} + 243 T^{8} + \cdots + 57\!\cdots\!20 \)
T^9 + 243*T^8 - 291547*T^7 - 84746425*T^6 + 17175252767*T^5 + 5633799483461*T^4 - 296253534364081*T^3 - 117316440305580971*T^2 + 223061274404557932*T + 573577985130202648620
$43$
\( T^{9} - 435 T^{8} + \cdots + 55\!\cdots\!48 \)
T^9 - 435*T^8 - 249717*T^7 + 98739771*T^6 + 20626805815*T^5 - 5605656872447*T^4 - 683675799144016*T^3 + 14961989597850608*T^2 + 2841294248911919360*T + 55103202861902466048
$47$
\( T^{9} - 133 T^{8} + \cdots + 11\!\cdots\!40 \)
T^9 - 133*T^8 - 445067*T^7 + 15330781*T^6 + 69831226190*T^5 + 2638189214060*T^4 - 4449722614356760*T^3 - 372239351325812624*T^2 + 98083863474254492064*T + 11090460084198278653440
$53$
\( T^{9} + 958 T^{8} + \cdots - 59\!\cdots\!40 \)
T^9 + 958*T^8 + 41798*T^7 - 226747842*T^6 - 86028415938*T^5 - 8229856967242*T^4 + 1061761458359309*T^3 + 213279003637789780*T^2 + 3550311604297044228*T - 590019594869432723040
$59$
\( T^{9} + 538 T^{8} + \cdots - 23\!\cdots\!68 \)
T^9 + 538*T^8 - 446020*T^7 - 202925590*T^6 + 54090417212*T^5 + 25428934030852*T^4 - 964613857232355*T^3 - 1035319391474991170*T^2 - 100856030990828468160*T - 2345374704186667227168
$61$
\( T^{9} - 1374 T^{8} + \cdots - 14\!\cdots\!16 \)
T^9 - 1374*T^8 - 15462*T^7 + 635070576*T^6 - 181238519680*T^5 - 36089971779226*T^4 + 10850353128423939*T^3 + 809983896570546850*T^2 + 13412942251861077780*T - 14821813261109394216
$67$
\( T^{9} - 752 T^{8} + \cdots - 53\!\cdots\!24 \)
T^9 - 752*T^8 - 758193*T^7 + 478093694*T^6 + 128201322179*T^5 - 54579217253748*T^4 - 8904750638938720*T^3 + 1532501979117352064*T^2 + 190676747151483138816*T - 5343458662283780404224
$71$
\( T^{9} - 418 T^{8} + \cdots + 57\!\cdots\!48 \)
T^9 - 418*T^8 - 1534813*T^7 + 833733656*T^6 + 660095495243*T^5 - 480047280319258*T^4 - 34327407036238488*T^3 + 77976118038990635680*T^2 - 15535982933989515254400*T + 575543475130295449525248
$73$
\( T^{9} - 2406 T^{8} + \cdots - 37\!\cdots\!00 \)
T^9 - 2406*T^8 + 1141888*T^7 + 963110194*T^6 - 632779518301*T^5 - 160134775093316*T^4 + 82919750525597700*T^3 + 13900781107950241680*T^2 - 2413790395653284050432*T - 377531084233802240345600
$79$
\( T^{9} + 486 T^{8} + \cdots - 26\!\cdots\!40 \)
T^9 + 486*T^8 - 3413980*T^7 - 1400175602*T^6 + 3779698647655*T^5 + 1179631560113860*T^4 - 1555694738139835460*T^3 - 178099601829562242496*T^2 + 239654763579716233897984*T - 26972038702706013991075840
$83$
\( T^{9} + 106 T^{8} + \cdots + 19\!\cdots\!12 \)
T^9 + 106*T^8 - 2901810*T^7 + 47205840*T^6 + 2703829550229*T^5 - 200778136808594*T^4 - 873823313065229732*T^3 + 59413078836121210664*T^2 + 57443773961706845386560*T + 1933206226766325832816512
$89$
\( T^{9} + 234 T^{8} + \cdots + 31\!\cdots\!76 \)
T^9 + 234*T^8 - 1779411*T^7 - 665259624*T^6 + 647996539079*T^5 + 219797975271628*T^4 - 68190794507107304*T^3 - 21464893753780750848*T^2 + 651332798802476040816*T + 317308517656079155200576
$97$
\( T^{9} - 2409 T^{8} + \cdots + 30\!\cdots\!96 \)
T^9 - 2409*T^8 + 1352*T^7 + 4451923950*T^6 - 3609547594611*T^5 - 716658166044497*T^4 + 1956133771581344370*T^3 - 690386345904675315076*T^2 - 14646987214172069195928*T + 30959210201065945183387296
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