[N,k,chi] = [230,4,Mod(139,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.139");
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
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\)
\(47\)
\(51\)
\(\chi(n)\)
\(-1\)
\(1\)
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
\( T_{3}^{14} + 223 T_{3}^{12} + 19539 T_{3}^{10} + 852894 T_{3}^{8} + 19553159 T_{3}^{6} + 231696639 T_{3}^{4} + 1302477653 T_{3}^{2} + 2723378596 \)
T3^14 + 223*T3^12 + 19539*T3^10 + 852894*T3^8 + 19553159*T3^6 + 231696639*T3^4 + 1302477653*T3^2 + 2723378596
acting on \(S_{4}^{\mathrm{new}}(230, [\chi])\).
$p$
$F_p(T)$
$2$
\( (T^{2} + 4)^{7} \)
(T^2 + 4)^7
$3$
\( T^{14} + 223 T^{12} + \cdots + 2723378596 \)
T^14 + 223*T^12 + 19539*T^10 + 852894*T^8 + 19553159*T^6 + 231696639*T^4 + 1302477653*T^2 + 2723378596
$5$
\( T^{14} + \cdots + 476837158203125 \)
T^14 + 6*T^13 + 161*T^12 - 1204*T^11 + 4471*T^10 - 177510*T^9 + 1743575*T^8 - 9147000*T^7 + 217946875*T^6 - 2773593750*T^5 + 8732421875*T^4 - 293945312500*T^3 + 4913330078125*T^2 + 22888183593750*T + 476837158203125
$7$
\( T^{14} + \cdots + 146581095556624 \)
T^14 + 2096*T^12 + 1578060*T^10 + 509973305*T^8 + 67486596460*T^6 + 3527972102360*T^4 + 64505469416944*T^2 + 146581095556624
$11$
\( (T^{7} + 73 T^{6} - 631 T^{5} + \cdots - 1520797760)^{2} \)
(T^7 + 73*T^6 - 631*T^5 - 109358*T^4 - 455360*T^3 + 38988576*T^2 + 198575596*T - 1520797760)^2
$13$
\( T^{14} + 17875 T^{12} + \cdots + 10\!\cdots\!44 \)
T^14 + 17875*T^12 + 123387971*T^10 + 413458452030*T^8 + 678391089469599*T^6 + 452490786891503211*T^4 + 34540243723768967469*T^2 + 107645601696022266244
$17$
\( T^{14} + 35676 T^{12} + \cdots + 33\!\cdots\!00 \)
T^14 + 35676*T^12 + 460795336*T^10 + 2808080791889*T^8 + 8422342016811800*T^6 + 11457269989496190028*T^4 + 5649153131362360459856*T^2 + 338931760654284336400
$19$
\( (T^{7} - 77 T^{6} + \cdots + 3897418182928)^{2} \)
(T^7 - 77*T^6 - 27117*T^5 + 1753538*T^4 + 180870142*T^3 - 9306645048*T^2 - 100904860052*T + 3897418182928)^2
$23$
\( (T^{2} + 529)^{7} \)
(T^2 + 529)^7
$29$
\( (T^{7} - 395 T^{6} + \cdots + 43908716160740)^{2} \)
(T^7 - 395*T^6 - 3712*T^5 + 16326882*T^4 - 1494071099*T^3 - 51881011787*T^2 + 6467467381706*T + 43908716160740)^2
$31$
\( (T^{7} + 160 T^{6} + \cdots - 108456344870975)^{2} \)
(T^7 + 160*T^6 - 42052*T^5 - 5149851*T^4 + 514231961*T^3 + 41479291658*T^2 - 1679247428902*T - 108456344870975)^2
$37$
\( T^{14} + 539049 T^{12} + \cdots + 32\!\cdots\!76 \)
T^14 + 539049*T^12 + 111087964296*T^10 + 11106103668950600*T^8 + 566735826376323633600*T^6 + 14024178583044045944439696*T^4 + 139786254022328560922954783424*T^2 + 322869246538526680411698729246976
$41$
\( (T^{7} + 952 T^{6} + \cdots - 44\!\cdots\!03)^{2} \)
(T^7 + 952*T^6 + 144276*T^5 - 104273579*T^4 - 41123402959*T^3 - 5435839306486*T^2 - 286383952230598*T - 4461048431070103)^2
$43$
\( T^{14} + 694656 T^{12} + \cdots + 30\!\cdots\!00 \)
T^14 + 694656*T^12 + 166880257660*T^10 + 17369480297490832*T^8 + 842208850329353435600*T^6 + 18809670132797588834495936*T^4 + 165076391961061981983530835200*T^2 + 307842915830657620095036520960000
$47$
\( T^{14} + 798808 T^{12} + \cdots + 34\!\cdots\!24 \)
T^14 + 798808*T^12 + 211245073374*T^10 + 21249691598777608*T^8 + 859978678870918600129*T^6 + 13102468072569422477994960*T^4 + 52586150165204505634265349696*T^2 + 34958607077950320699988884418624
$53$
\( T^{14} + 966577 T^{12} + \cdots + 17\!\cdots\!36 \)
T^14 + 966577*T^12 + 339190483192*T^10 + 53783511939144944*T^8 + 4039634776672226711040*T^6 + 149608005546401349362876160*T^4 + 2634682373323095030939336448000*T^2 + 17525485127807420668843223095054336
$59$
\( (T^{7} - 1407 T^{6} + \cdots - 30\!\cdots\!40)^{2} \)
(T^7 - 1407*T^6 + 395292*T^5 + 219942096*T^4 - 133963830592*T^3 + 17570394341952*T^2 + 1352168743838400*T - 306214699126946240)^2
$61$
\( (T^{7} + 1871 T^{6} + \cdots - 35\!\cdots\!00)^{2} \)
(T^7 + 1871*T^6 + 790365*T^5 - 202966384*T^4 - 107616895766*T^3 + 11760074125908*T^2 + 3443682965165420*T - 353194702681136200)^2
$67$
\( T^{14} + 1206121 T^{12} + \cdots + 73\!\cdots\!00 \)
T^14 + 1206121*T^12 + 537642031896*T^10 + 107590701060929640*T^8 + 9344919338809299583168*T^6 + 299752873173448334706144784*T^4 + 1038645926381954989934367227840*T^2 + 730383308801113103167981788217600
$71$
\( (T^{7} + 1904 T^{6} + \cdots + 63\!\cdots\!93)^{2} \)
(T^7 + 1904*T^6 - 173482*T^5 - 2294009991*T^4 - 1392412886391*T^3 - 129245498346378*T^2 + 53088774775260400*T + 6375361089013134193)^2
$73$
\( T^{14} + 1885088 T^{12} + \cdots + 16\!\cdots\!96 \)
T^14 + 1885088*T^12 + 1337740543966*T^10 + 446783836058135192*T^8 + 71539814890388725564913*T^6 + 4748797719681819945309533304*T^4 + 61694294172688581324319111496720*T^2 + 160745748139827619574910045724324096
$79$
\( (T^{7} + 764 T^{6} + \cdots + 25\!\cdots\!32)^{2} \)
(T^7 + 764*T^6 - 1202882*T^5 - 960259724*T^4 + 227665705692*T^3 + 258294797901552*T^2 + 40155721569516640*T + 257926872164009632)^2
$83$
\( T^{14} + 2532285 T^{12} + \cdots + 42\!\cdots\!04 \)
T^14 + 2532285*T^12 + 2353718926896*T^10 + 988178783732744092*T^8 + 190906379488585214507824*T^6 + 17101181747315684347903110096*T^4 + 618499192149124195487985325675456*T^2 + 4274564711133877384655937314407938304
$89$
\( (T^{7} - 1168 T^{6} + \cdots + 40\!\cdots\!00)^{2} \)
(T^7 - 1168*T^6 - 3050274*T^5 + 3794613044*T^4 + 1703867755788*T^3 - 2359976360272496*T^2 - 255604711463700800*T + 408730197265475020000)^2
$97$
\( T^{14} + 6164419 T^{12} + \cdots + 57\!\cdots\!44 \)
T^14 + 6164419*T^12 + 14865762561577*T^10 + 18037700754978417688*T^8 + 11874313831906591931018600*T^6 + 4272443157647622417590043588736*T^4 + 784987802525996177498532391733404560*T^2 + 57311000038598084137977576198147513722944
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