[N,k,chi] = [26,7,Mod(5,26)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(26, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("26.5");
S:= CuspForms(chi, 7);
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 \(\left(\mathbb{Z}/26\mathbb{Z}\right)^\times\).
\(n\)
\(15\)
\(\chi(n)\)
\(-\beta_{3}\)
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
\( T_{3}^{4} - 2613T_{3}^{2} + 9738T_{3} + 74880 \)
T3^4 - 2613*T3^2 + 9738*T3 + 74880
acting on \(S_{7}^{\mathrm{new}}(26, [\chi])\).
$p$
$F_p(T)$
$2$
\( (T^{2} + 8 T + 32)^{4} \)
(T^2 + 8*T + 32)^4
$3$
\( (T^{4} - 2613 T^{2} + 9738 T + 74880)^{2} \)
(T^4 - 2613*T^2 + 9738*T + 74880)^2
$5$
\( T^{8} - 84 T^{7} + \cdots + 12\!\cdots\!00 \)
T^8 - 84*T^7 + 3528*T^6 + 1022880*T^5 + 306720525*T^4 - 11569477500*T^3 + 412867845000*T^2 + 100888190325000*T + 12326495112562500
$7$
\( T^{8} + 230 T^{7} + \cdots + 14\!\cdots\!44 \)
T^8 + 230*T^7 + 26450*T^6 - 26391076*T^5 + 58109785393*T^4 + 7018076369842*T^3 + 425398187637698*T^2 - 3542468528182232*T + 14749808106668944
$11$
\( T^{8} + 246 T^{7} + \cdots + 22\!\cdots\!84 \)
T^8 + 246*T^7 + 30258*T^6 + 3368583864*T^5 + 25959845033940*T^4 + 24874692495683544*T^3 + 11007359987301780552*T^2 - 6993615083612080064544*T + 2221724918334201060216384
$13$
\( T^{8} - 4050 T^{7} + \cdots + 54\!\cdots\!61 \)
T^8 - 4050*T^7 + 9030346*T^6 - 10283861250*T^5 - 341489425134*T^4 - 49638234036251250*T^3 + 210389769793455808426*T^2 - 455444398155427442172450*T + 542800770374370512771595361
$17$
\( T^{8} + 121018950 T^{6} + \cdots + 55\!\cdots\!16 \)
T^8 + 121018950*T^6 + 4187250611767113*T^4 + 32365879952334406182180*T^2 + 55483488935197612027090108416
$19$
\( T^{8} - 6358 T^{7} + \cdots + 52\!\cdots\!36 \)
T^8 - 6358*T^7 + 20212082*T^6 - 227591573560*T^5 + 4851217110005536*T^4 - 39509541504175073120*T^3 + 179047429034068646347808*T^2 - 433735303146887323666557824*T + 525353293847425459387174318336
$23$
\( T^{8} + 704959452 T^{6} + \cdots + 36\!\cdots\!04 \)
T^8 + 704959452*T^6 + 110629731372555300*T^4 + 5212399429441652128720128*T^2 + 36240532685674263180489909141504
$29$
\( (T^{4} - 15966 T^{3} + \cdots - 11\!\cdots\!36)^{2} \)
(T^4 - 15966*T^3 - 169366062*T^2 + 3354985896348*T - 11989344407516736)^2
$31$
\( T^{8} - 69374 T^{7} + \cdots + 27\!\cdots\!96 \)
T^8 - 69374*T^7 + 2406375938*T^6 - 16368217921928*T^5 + 4094292390869669728*T^4 - 276200337635212573255456*T^3 + 9442674809549835416909418272*T^2 - 72103714297626779268279153960832*T + 275289879211759063965520314136996096
$37$
\( T^{8} - 108500 T^{7} + \cdots + 56\!\cdots\!44 \)
T^8 - 108500*T^7 + 5886125000*T^6 + 10202833671904*T^5 + 520688854918781773*T^4 - 72069626856416085165628*T^3 + 4806763735230599906630505608*T^2 + 23273524951609744679986453568648*T + 56343206522008917931734287886373444
$41$
\( T^{8} - 91152 T^{7} + \cdots + 61\!\cdots\!96 \)
T^8 - 91152*T^7 + 4154343552*T^6 + 103454296885344*T^5 + 5790994732363434708*T^4 - 415096179307791710721408*T^3 + 19130461082224277945665978368*T^2 + 486383415115234039880169756450816*T + 6183040374258780698775320690138527296
$43$
\( T^{8} + 10542744582 T^{6} + \cdots + 33\!\cdots\!24 \)
T^8 + 10542744582*T^6 + 30055253987164091985*T^4 + 21476387932041622122830107728*T^2 + 3333737942516858754212232391661773824
$47$
\( T^{8} + 609198 T^{7} + \cdots + 24\!\cdots\!00 \)
T^8 + 609198*T^7 + 185561101602*T^6 + 31791099065818788*T^5 + 3294133243485236414721*T^4 + 181300018267305933592419090*T^3 + 4521604949868588727669262201250*T^2 - 47016908406566019491389413867819000*T + 244447458437923102621375533658914800400
$53$
\( (T^{4} + 154896 T^{3} + \cdots + 71\!\cdots\!60)^{2} \)
(T^4 + 154896*T^3 - 18482683806*T^2 - 1844031518661936*T + 71053259137691844360)^2
$59$
\( T^{8} + 277602 T^{7} + \cdots + 17\!\cdots\!16 \)
T^8 + 277602*T^7 + 38531435202*T^6 + 7354752426384216*T^5 + 11916175020361559022288*T^4 + 3647114780520965490421031808*T^3 + 580345223276130876289052553149568*T^2 + 45236788107411446794692505002101313024*T + 1763060085790670024613546167771516963644416
$61$
\( (T^{4} + 213516 T^{3} + \cdots + 14\!\cdots\!24)^{2} \)
(T^4 + 213516*T^3 - 105812774520*T^2 - 5284606508604144*T + 1483447266440910598224)^2
$67$
\( T^{8} - 908626 T^{7} + \cdots + 15\!\cdots\!64 \)
T^8 - 908626*T^7 + 412800603938*T^6 - 111455074706558824*T^5 + 19527320918698290206260*T^4 - 2215662062356053766337763944*T^3 + 163435127462840779425960399260552*T^2 - 7198526718153552210686253268579570016*T + 158530138888753471017698271738232881062464
$71$
\( T^{8} + 1084182 T^{7} + \cdots + 16\!\cdots\!00 \)
T^8 + 1084182*T^7 + 587725304562*T^6 + 144847726264927572*T^5 + 26734468264452961101201*T^4 + 10430905765740729511885758810*T^3 + 6086908673943269876123810332072050*T^2 + 1418970850868374587881567634051756207000*T + 165394158469419859832139362673739109146890000
$73$
\( T^{8} + 425948 T^{7} + \cdots + 27\!\cdots\!00 \)
T^8 + 425948*T^7 + 90715849352*T^6 - 49449919993359496*T^5 + 12029469509207906272516*T^4 - 295611655805744067849557888*T^3 + 5468556325900731985087349399552*T^2 - 5475491874265814903953299947281756160*T + 2741218109352906857995081270885998877926400
$79$
\( (T^{4} - 385350 T^{3} + \cdots - 18\!\cdots\!40)^{2} \)
(T^4 - 385350*T^3 - 303960200994*T^2 + 161192199850375740*T - 18754387827901893885840)^2
$83$
\( T^{8} - 1160634 T^{7} + \cdots + 46\!\cdots\!64 \)
T^8 - 1160634*T^7 + 673535640978*T^6 - 194129950816696296*T^5 + 29465877240559087888980*T^4 - 1857893025615869738555543016*T^3 + 1153234201740083638913112860269512*T^2 - 327038579191072398183765112921021635744*T + 46371427468043788378983161683363428433664064
$89$
\( T^{8} + 2041320 T^{7} + \cdots + 45\!\cdots\!00 \)
T^8 + 2041320*T^7 + 2083493671200*T^6 + 805653230444775936*T^5 + 117651961662958207521876*T^4 - 23913126975055917035904484896*T^3 + 30597101977292022157928671963264128*T^2 + 5300708438391645460667402061419237147520*T + 459153124529396192426071404021153906644558400
$97$
\( T^{8} + 2254048 T^{7} + \cdots + 11\!\cdots\!00 \)
T^8 + 2254048*T^7 + 2540366193152*T^6 + 68445291171310192*T^5 + 2865074894519581904269960*T^4 + 5803890605644767218871874081280*T^3 + 5806250987928060746552144313191245952*T^2 + 1142215735033668154490851090998362880666560*T + 112349327308710157856576832549374278448651568400
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