[N,k,chi] = [1100,2,Mod(201,1100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1100, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1100.201");
S:= CuspForms(chi, 2);
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 \(\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times\).
\(n\)
\(101\)
\(177\)
\(551\)
\(\chi(n)\)
\(-\beta_{8}\)
\(1\)
\(1\)
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
\( T_{3}^{16} - 2 T_{3}^{15} + 8 T_{3}^{14} + 5 T_{3}^{13} + 19 T_{3}^{12} + 16 T_{3}^{11} + 389 T_{3}^{10} + 602 T_{3}^{9} + 1231 T_{3}^{8} + 567 T_{3}^{7} + 659 T_{3}^{6} + 199 T_{3}^{5} + 1251 T_{3}^{4} - 30 T_{3}^{3} + 1040 T_{3}^{2} + \cdots + 400 \)
T3^16 - 2*T3^15 + 8*T3^14 + 5*T3^13 + 19*T3^12 + 16*T3^11 + 389*T3^10 + 602*T3^9 + 1231*T3^8 + 567*T3^7 + 659*T3^6 + 199*T3^5 + 1251*T3^4 - 30*T3^3 + 1040*T3^2 + 400
acting on \(S_{2}^{\mathrm{new}}(1100, [\chi])\).
$p$
$F_p(T)$
$2$
\( T^{16} \)
T^16
$3$
\( T^{16} - 2 T^{15} + 8 T^{14} + 5 T^{13} + \cdots + 400 \)
T^16 - 2*T^15 + 8*T^14 + 5*T^13 + 19*T^12 + 16*T^11 + 389*T^10 + 602*T^9 + 1231*T^8 + 567*T^7 + 659*T^6 + 199*T^5 + 1251*T^4 - 30*T^3 + 1040*T^2 + 400
$5$
\( T^{16} \)
T^16
$7$
\( T^{16} + 26 T^{14} + 10 T^{13} + \cdots + 281961 \)
T^16 + 26*T^14 + 10*T^13 + 373*T^12 + 740*T^11 + 4300*T^10 + 17260*T^9 + 68121*T^8 + 196900*T^7 + 500680*T^6 + 1025110*T^5 + 1810837*T^4 + 2454240*T^3 + 2340882*T^2 + 1194750*T + 281961
$11$
\( T^{16} + 5 T^{15} + 37 T^{14} + \cdots + 214358881 \)
T^16 + 5*T^15 + 37*T^14 + 105*T^13 + 558*T^12 + 1305*T^11 + 8259*T^10 + 22285*T^9 + 115890*T^8 + 245135*T^7 + 999339*T^6 + 1736955*T^5 + 8169678*T^4 + 16910355*T^3 + 65547757*T^2 + 97435855*T + 214358881
$13$
\( T^{16} + T^{15} + 56 T^{14} + 107 T^{13} + \cdots + 121 \)
T^16 + T^15 + 56*T^14 + 107*T^13 + 1347*T^12 + 2761*T^11 + 10387*T^10 + 25957*T^9 + 94736*T^8 - 27723*T^7 + 471947*T^6 + 2011096*T^5 + 3307692*T^4 - 470338*T^3 + 490381*T^2 + 12496*T + 121
$17$
\( T^{16} + 8 T^{15} + 99 T^{14} + \cdots + 126990361 \)
T^16 + 8*T^15 + 99*T^14 + 746*T^13 + 6829*T^12 + 23992*T^11 + 229216*T^10 + 468763*T^9 + 3770073*T^8 + 3479111*T^7 + 29855809*T^6 - 8691264*T^5 + 265302849*T^4 - 888219938*T^3 + 3086175811*T^2 - 1000901311*T + 126990361
$19$
\( T^{16} - 13 T^{15} + 143 T^{14} + \cdots + 61716736 \)
T^16 - 13*T^15 + 143*T^14 - 863*T^13 + 5099*T^12 - 27988*T^11 + 218527*T^10 - 917802*T^9 + 6366513*T^8 - 42378657*T^7 + 210748612*T^6 - 312196204*T^5 + 616882985*T^4 - 219153404*T^3 + 307631024*T^2 + 228735296*T + 61716736
$23$
\( (T^{8} + 8 T^{7} - 76 T^{6} - 638 T^{5} + \cdots + 15831)^{2} \)
(T^8 + 8*T^7 - 76*T^6 - 638*T^5 + 833*T^4 + 7598*T^3 - 8782*T^2 - 13380*T + 15831)^2
$29$
\( T^{16} + 7 T^{15} + \cdots + 7743120025 \)
T^16 + 7*T^15 + 68*T^14 + 225*T^13 + 3259*T^12 + 17099*T^11 + 231469*T^10 + 750023*T^9 + 10046226*T^8 + 43355743*T^7 + 125702049*T^6 - 546611404*T^5 + 1999183466*T^4 + 1374675250*T^3 + 14313045335*T^2 + 6520429500*T + 7743120025
$31$
\( T^{16} - 2 T^{15} + \cdots + 4381778025 \)
T^16 - 2*T^15 + T^14 + 96*T^13 + 8636*T^12 - 39936*T^11 + 707421*T^10 - 965707*T^9 + 17025514*T^8 - 5415675*T^7 + 183047007*T^6 + 114424639*T^5 + 661174801*T^4 + 275771295*T^3 + 3227999940*T^2 - 5863222125*T + 4381778025
$37$
\( T^{16} + 8 T^{15} + \cdots + 122696778961 \)
T^16 + 8*T^15 + 96*T^14 + 328*T^13 + 6564*T^12 + 75592*T^11 + 1026962*T^10 + 6975784*T^9 + 56660358*T^8 + 288939372*T^7 + 1412154148*T^6 + 2389311144*T^5 + 6389748869*T^4 - 39715882796*T^3 + 116145979474*T^2 - 124974656304*T + 122696778961
$41$
\( T^{16} + 15 T^{15} + \cdots + 3401222400 \)
T^16 + 15*T^15 + 215*T^14 + 1587*T^13 + 12145*T^12 + 48480*T^11 + 345384*T^10 + 301140*T^9 + 6532960*T^8 - 18554592*T^7 + 104477040*T^6 - 64419840*T^5 + 233534016*T^4 + 582500160*T^3 + 2536220160*T^2 - 4912876800*T + 3401222400
$43$
\( (T^{8} - 134 T^{6} - 240 T^{5} + \cdots - 71125)^{2} \)
(T^8 - 134*T^6 - 240*T^5 + 4084*T^4 + 14380*T^3 - 8970*T^2 - 80700*T - 71125)^2
$47$
\( T^{16} + 18 T^{15} + \cdots + 4287363654025 \)
T^16 + 18*T^15 + 261*T^14 + 1926*T^13 + 18886*T^12 + 57014*T^11 + 1169021*T^10 - 2157667*T^9 + 29030084*T^8 - 28657465*T^7 + 1233060007*T^6 - 9880815581*T^5 + 80245540061*T^4 - 270730954985*T^3 + 707303351960*T^2 - 1231724494675*T + 4287363654025
$53$
\( T^{16} + 6 T^{15} + \cdots + 4303360000 \)
T^16 + 6*T^15 + 128*T^14 + 765*T^13 + 11151*T^12 + 77600*T^11 + 931887*T^10 + 7679872*T^9 + 92117171*T^8 + 593994145*T^7 + 2916510455*T^6 + 7024378925*T^5 + 7678303425*T^4 - 35831948000*T^3 + 44466928000*T^2 + 5943360000*T + 4303360000
$59$
\( T^{16} - 6 T^{15} + \cdots + 1870130025 \)
T^16 - 6*T^15 + 177*T^14 - 590*T^13 + 14734*T^12 - 125042*T^11 + 1446311*T^10 - 10568991*T^9 + 179798846*T^8 - 1115857679*T^7 + 4617776551*T^6 - 11728999407*T^5 + 18974730601*T^4 - 12431698275*T^3 + 7274760390*T^2 - 4082111775*T + 1870130025
$61$
\( T^{16} - 24 T^{15} + \cdots + 8406166636921 \)
T^16 - 24*T^15 + 276*T^14 - 1406*T^13 + 23339*T^12 - 191212*T^11 + 1806862*T^10 - 9366928*T^9 + 235856879*T^8 - 325225944*T^7 + 12471951486*T^6 + 13028292052*T^5 + 280501719303*T^4 + 544356568818*T^3 + 2979160662056*T^2 + 7005916370176*T + 8406166636921
$67$
\( (T^{8} - 9 T^{7} - 177 T^{6} + \cdots + 1920301)^{2} \)
(T^8 - 9*T^7 - 177*T^6 + 1530*T^5 + 9376*T^4 - 73130*T^3 - 176193*T^2 + 851017*T + 1920301)^2
$71$
\( T^{16} - 36 T^{15} + \cdots + 5027034831025 \)
T^16 - 36*T^15 + 755*T^14 - 10366*T^13 + 108083*T^12 - 822216*T^11 + 5128380*T^10 - 23074455*T^9 + 99591807*T^8 - 207886377*T^7 + 1196110801*T^6 + 4668082042*T^5 + 38533434881*T^4 + 149779890170*T^3 + 1217074746785*T^2 + 3631997100025*T + 5027034831025
$73$
\( T^{16} + 9 T^{15} + \cdots + 57739557809025 \)
T^16 + 9*T^15 + 345*T^14 + 4354*T^13 + 75973*T^12 + 321184*T^11 + 7319895*T^10 - 11141510*T^9 + 454970932*T^8 - 2083037462*T^7 + 13222803861*T^6 - 41532287563*T^5 + 328083621451*T^4 + 36799704645*T^3 - 547096228560*T^2 - 7318758543075*T + 57739557809025
$79$
\( T^{16} + \cdots + 610938937718041 \)
T^16 + 45*T^15 + 1396*T^14 + 29839*T^13 + 521225*T^12 + 7293023*T^11 + 88598395*T^10 + 822036709*T^9 + 6063842682*T^8 + 30434648381*T^7 + 103389814227*T^6 + 280486796290*T^5 + 1923722057204*T^4 + 7886600185012*T^3 + 21817285604577*T^2 + 72362903058844*T + 610938937718041
$83$
\( T^{16} + 14 T^{15} + \cdots + 1162689914961 \)
T^16 + 14*T^15 + 203*T^14 + 2288*T^13 + 43262*T^12 + 712*T^11 + 2617877*T^10 - 154781*T^9 + 42006350*T^8 - 267422167*T^7 + 1664808741*T^6 - 7780105997*T^5 + 55565208433*T^4 - 228877402533*T^3 + 649936790010*T^2 - 1096589133099*T + 1162689914961
$89$
\( (T^{8} - 9 T^{7} - 306 T^{6} + \cdots - 570901)^{2} \)
(T^8 - 9*T^7 - 306*T^6 + 2363*T^5 + 13868*T^4 - 75843*T^3 - 119014*T^2 + 672961*T - 570901)^2
$97$
\( T^{16} - 49 T^{15} + \cdots + 10719703296 \)
T^16 - 49*T^15 + 1315*T^14 - 26521*T^13 + 474577*T^12 - 6832640*T^11 + 72643948*T^10 - 558806620*T^9 + 3579053648*T^8 - 20248441392*T^7 + 89164625360*T^6 - 187543206368*T^5 + 389656442176*T^4 - 298957766592*T^3 + 315338481792*T^2 + 96686058240*T + 10719703296
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