[N,k,chi] = [25,38,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 38);
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 48\sqrt{63737521}\).
We also show the integral \(q\)-expansion of the trace form .
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 does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} - 194400T_{2} - 137403408384 \)
T2^2 - 194400*T2 - 137403408384
acting on \(S_{38}^{\mathrm{new}}(\Gamma_0(25))\).
$p$
$F_p(T)$
$2$
\( T^{2} - 194400 T - 137403408384 \)
T^2 - 194400*T - 137403408384
$3$
\( T^{2} + \cdots - 712337053132656 \)
T^2 + 13991400*T - 712337053132656
$5$
\( T^{2} \)
T^2
$7$
\( T^{2} + \cdots - 10\!\cdots\!64 \)
T^2 - 3448443953486000*T - 10702226241775613267523488752064
$11$
\( T^{2} + \cdots + 26\!\cdots\!84 \)
T^2 + 26734036354848538056*T + 26545401766395881323605638597176064784
$13$
\( T^{2} + \cdots - 66\!\cdots\!76 \)
T^2 + 530581741653933178300*T - 6690967700061658655245109989374887671676
$17$
\( T^{2} + \cdots + 19\!\cdots\!76 \)
T^2 - 89439073881931767332700*T + 1910726350504571161153534634660677831625579076
$19$
\( T^{2} + \cdots - 21\!\cdots\!00 \)
T^2 - 373276466572513713706120*T - 210670237767637237999202183475770087205956476400
$23$
\( T^{2} + \cdots + 21\!\cdots\!04 \)
T^2 - 26241180149933881945462800*T + 2143870671211642813067011165591078020769191280704
$29$
\( T^{2} + \cdots - 37\!\cdots\!00 \)
T^2 + 1270673827125882417951629220*T - 378820335538613904791939418010749502909605184443987900
$31$
\( T^{2} + \cdots - 61\!\cdots\!56 \)
T^2 - 261420819791418895481545024*T - 6119118623007074558772879178217954449470261132761209856
$37$
\( T^{2} + \cdots - 80\!\cdots\!44 \)
T^2 - 68025363793820786588733238100*T - 8096016842066207433199112501503435975633718054027354319644
$41$
\( T^{2} + \cdots + 34\!\cdots\!24 \)
T^2 + 1260483295466373133974684841836*T + 347403162942669272863038069448218707180091796980680187962724
$43$
\( T^{2} + \cdots - 10\!\cdots\!36 \)
T^2 - 2570241023157918831169581605000*T - 1035163211200960184740304426437289116361044797832383386660336
$47$
\( T^{2} + \cdots + 23\!\cdots\!96 \)
T^2 + 4252206875568934025158407583200*T + 2397100503536879055519177994480638349840546260801633950474496
$53$
\( T^{2} + \cdots + 44\!\cdots\!44 \)
T^2 + 159799736258590810071505678893900*T + 4427835343123808113583438306435244645152743876261075933728782244
$59$
\( T^{2} + \cdots - 19\!\cdots\!00 \)
T^2 + 237962459606090128758899369700840*T - 19951828174327687524934253537468494206925274640386475633863583600
$61$
\( T^{2} + \cdots - 12\!\cdots\!16 \)
T^2 - 101798841373038700200106255199644*T - 1232264205902282318731078025647392967139054625813669836891025568316
$67$
\( T^{2} + \cdots + 20\!\cdots\!76 \)
T^2 - 10891923280981358108643809352546200*T + 20642145835298439893651056831318600638798170269548798523255069829776
$71$
\( T^{2} + \cdots - 44\!\cdots\!36 \)
T^2 + 746133089793832492689962158868016*T - 44420510421447279863982328659884765457480334218806413941108773055936
$73$
\( T^{2} + \cdots + 96\!\cdots\!04 \)
T^2 + 19639851676496426023909382507487700*T + 96226119118682588187013543718354337076868120587717217120589598725604
$79$
\( T^{2} + \cdots + 18\!\cdots\!00 \)
T^2 - 272401638034095839035647945144674080*T + 18305626494011330814755672971002224685372017853979279455158236824121600
$83$
\( T^{2} + \cdots + 46\!\cdots\!84 \)
T^2 - 470460275390909929308746217601073400*T + 46966680845967720073148003351617371174272057708157531111350440501050384
$89$
\( T^{2} + \cdots - 35\!\cdots\!00 \)
T^2 + 1332868921711238117914343978794942860*T - 356384782335093371177228915399085955418359919433966084817996665901115100
$97$
\( T^{2} + \cdots - 75\!\cdots\!04 \)
T^2 + 6002061888473229973039130090661237700*T - 7579754079337004818054736044949219236104340954017188363769763251490247804
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