[N,k,chi] = [98,12,Mod(1,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.1");
S:= CuspForms(chi, 12);
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
\(2\)
\(1\)
\(7\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} - 266T_{3}^{3} - 570840T_{3}^{2} + 100589202T_{3} + 23777531775 \)
T3^4 - 266*T3^3 - 570840*T3^2 + 100589202*T3 + 23777531775
acting on \(S_{12}^{\mathrm{new}}(\Gamma_0(98))\).
$p$
$F_p(T)$
$2$
\( (T + 32)^{4} \)
(T + 32)^4
$3$
\( T^{4} - 266 T^{3} + \cdots + 23777531775 \)
T^4 - 266*T^3 - 570840*T^2 + 100589202*T + 23777531775
$5$
\( T^{4} + \cdots - 348755924545875 \)
T^4 + 3808*T^3 - 128983190*T^2 - 707019520200*T - 348755924545875
$7$
\( T^{4} \)
T^4
$11$
\( T^{4} + 920150 T^{3} + \cdots - 93\!\cdots\!25 \)
T^4 + 920150*T^3 + 108143336728*T^2 - 60914416625810286*T - 9332957949581479863825
$13$
\( T^{4} - 498736 T^{3} + \cdots + 24\!\cdots\!40 \)
T^4 - 498736*T^3 - 4054630895144*T^2 + 1751795111703572544*T + 2408090180050899802596240
$17$
\( T^{4} + 1333724 T^{3} + \cdots + 29\!\cdots\!45 \)
T^4 + 1333724*T^3 - 50309361485090*T^2 - 23033964273079382868*T + 296237818194979288466706345
$19$
\( T^{4} - 21551726 T^{3} + \cdots + 11\!\cdots\!55 \)
T^4 - 21551726*T^3 + 33741817505016*T^2 + 190530661872344653174*T + 114404066868772792292629855
$23$
\( T^{4} + 72510158 T^{3} + \cdots - 63\!\cdots\!09 \)
T^4 + 72510158*T^3 + 595932629174092*T^2 - 42774669343869373098342*T - 637907167691437696032893877909
$29$
\( T^{4} - 106787552 T^{3} + \cdots - 20\!\cdots\!32 \)
T^4 - 106787552*T^3 - 33972485772246344*T^2 + 5483788042461290061917952*T - 205116648499162708442075548469232
$31$
\( T^{4} - 194359774 T^{3} + \cdots - 67\!\cdots\!05 \)
T^4 - 194359774*T^3 - 8685623781317828*T^2 + 2757402172399368815344758*T - 67312154541198630352996675408005
$37$
\( T^{4} + 171517048 T^{3} + \cdots + 15\!\cdots\!21 \)
T^4 + 171517048*T^3 - 826922188007951358*T^2 - 55257560765618668313230112*T + 158364213999227147783477335041640021
$41$
\( T^{4} + 1656047568 T^{3} + \cdots - 13\!\cdots\!48 \)
T^4 + 1656047568*T^3 + 329083932629864088*T^2 - 386644310551725075232350912*T - 130359123642847764171552011144404848
$43$
\( T^{4} - 425139824 T^{3} + \cdots - 42\!\cdots\!40 \)
T^4 - 425139824*T^3 - 254940072096315936*T^2 + 106428213270795039787681024*T - 4216716101027728278389987898218240
$47$
\( T^{4} + 2223880974 T^{3} + \cdots - 11\!\cdots\!05 \)
T^4 + 2223880974*T^3 - 189464136164208180*T^2 - 1635576268123276398349861158*T - 117498776102222834377249521226042005
$53$
\( T^{4} - 7185483360 T^{3} + \cdots - 10\!\cdots\!79 \)
T^4 - 7185483360*T^3 + 6927893177188118922*T^2 + 8812785452834882828002730040*T - 10044344444625098664201938910901484979
$59$
\( T^{4} + 6997401502 T^{3} + \cdots + 13\!\cdots\!75 \)
T^4 + 6997401502*T^3 - 30249961025831220416*T^2 - 103689374918302800561801260982*T + 135359297130590751633889031725713618375
$61$
\( T^{4} - 6476463280 T^{3} + \cdots - 22\!\cdots\!95 \)
T^4 - 6476463280*T^3 - 44485055260218964598*T^2 + 307493129197302499066185751272*T - 227107553183913619442674168554197427795
$67$
\( T^{4} - 18660972186 T^{3} + \cdots + 13\!\cdots\!15 \)
T^4 - 18660972186*T^3 + 102148500672681412984*T^2 - 208516195904944430723799931614*T + 135639593371003788384490815778604509615
$71$
\( T^{4} - 11612224624 T^{3} + \cdots + 23\!\cdots\!40 \)
T^4 - 11612224624*T^3 - 72768654772381942976*T^2 - 92953326152576657300696411136*T + 2355223450598163135282929173158666240
$73$
\( T^{4} + 3731641452 T^{3} + \cdots - 63\!\cdots\!35 \)
T^4 + 3731641452*T^3 - 502150461325612181954*T^2 - 4405695142821218222648902856388*T - 6398052302569220754436639394402455773335
$79$
\( T^{4} + 12221157926 T^{3} + \cdots + 53\!\cdots\!75 \)
T^4 + 12221157926*T^3 - 1645441763552305282412*T^2 - 14327243738900927877033269031870*T + 533729876071728793484092455844318871914275
$83$
\( T^{4} - 158369761984 T^{3} + \cdots + 54\!\cdots\!00 \)
T^4 - 158369761984*T^3 + 8310665819585900471776*T^2 - 153543457680538436316502097823744*T + 543015288189063309573825707030689916064000
$89$
\( T^{4} - 71204406084 T^{3} + \cdots - 93\!\cdots\!75 \)
T^4 - 71204406084*T^3 + 1453465725500673388206*T^2 - 3910938042359911596232286290644*T - 93680231748098910801568394837389270885575
$97$
\( T^{4} - 344125898592 T^{3} + \cdots - 56\!\cdots\!00 \)
T^4 - 344125898592*T^3 + 34900138757573227814392*T^2 - 482488792431499969663332134945280*T - 56543863376293155740127108999232830089846000
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