Properties

Label 7581.2.a.bv
Level $7581$
Weight $2$
Character orbit 7581.a
Self dual yes
Analytic conductor $60.535$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7581,2,Mod(1,7581)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7581, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7581.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7581 = 3 \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7581.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(60.5345897723\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 4 x^{19} - 23 x^{18} + 104 x^{17} + 205 x^{16} - 1126 x^{15} - 840 x^{14} + 6598 x^{13} + 1081 x^{12} - 22764 x^{11} + 3513 x^{10} + 47144 x^{9} - 15486 x^{8} - 57360 x^{7} + \cdots + 281 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{19}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + \beta_1 q^{2} + q^{3} + (\beta_{2} + 1) q^{4} + \beta_{12} q^{5} + \beta_1 q^{6} - q^{7} + ( - \beta_{11} + \beta_{10} + \beta_1) q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + \beta_1 q^{2} + q^{3} + (\beta_{2} + 1) q^{4} + \beta_{12} q^{5} + \beta_1 q^{6} - q^{7} + ( - \beta_{11} + \beta_{10} + \beta_1) q^{8} + q^{9} + (\beta_{14} + \beta_{12} - \beta_{5} - 1) q^{10} + \beta_{15} q^{11} + (\beta_{2} + 1) q^{12} + (\beta_{19} + \beta_{17} - \beta_{15} + \beta_{13} + \beta_{12} + \beta_{10} + \beta_{7} + \beta_{3} + \beta_{2} - 1) q^{13} - \beta_1 q^{14} + \beta_{12} q^{15} + (\beta_{18} + \beta_{16} - \beta_{11} + \beta_{6} + \beta_{5} + \beta_1 + 1) q^{16} + ( - \beta_{17} + \beta_{13} - \beta_{12} - \beta_{8} - \beta_{4} - \beta_{2}) q^{17} + \beta_1 q^{18} + (\beta_{19} - \beta_{15} + 2 \beta_{13} + 2 \beta_{12} + \beta_{11} - \beta_{9} - \beta_{5} + \beta_{2} - 1) q^{20} - q^{21} + (\beta_{13} - \beta_{9} + \beta_{6} + \beta_{5} - \beta_{4}) q^{22} + (\beta_{19} + \beta_{17} - \beta_{15} + \beta_{14} + \beta_{12} - \beta_{11} + 2 \beta_{10} + \beta_{8} + 2 \beta_{7} + \cdots - 1) q^{23}+ \cdots + \beta_{15} q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{2} + 20 q^{3} + 22 q^{4} - 2 q^{5} + 4 q^{6} - 20 q^{7} + 12 q^{8} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{2} + 20 q^{3} + 22 q^{4} - 2 q^{5} + 4 q^{6} - 20 q^{7} + 12 q^{8} + 20 q^{9} - 20 q^{10} + 8 q^{11} + 22 q^{12} - 4 q^{14} - 2 q^{15} + 10 q^{16} + 6 q^{17} + 4 q^{18} - 18 q^{20} - 20 q^{21} - 4 q^{22} - 4 q^{23} + 12 q^{24} + 26 q^{25} - 12 q^{26} + 20 q^{27} - 22 q^{28} + 14 q^{29} - 20 q^{30} + 36 q^{31} + 38 q^{32} + 8 q^{33} + 24 q^{34} + 2 q^{35} + 22 q^{36} + 8 q^{37} - 20 q^{40} + 20 q^{41} - 4 q^{42} - 4 q^{44} - 2 q^{45} + 40 q^{46} - 14 q^{47} + 10 q^{48} + 20 q^{49} + 80 q^{50} + 6 q^{51} + 8 q^{52} + 22 q^{53} + 4 q^{54} + 24 q^{55} - 12 q^{56} + 22 q^{58} + 44 q^{59} - 18 q^{60} + 28 q^{61} + 34 q^{62} - 20 q^{63} + 32 q^{64} + 36 q^{65} - 4 q^{66} + 52 q^{67} + 36 q^{68} - 4 q^{69} + 20 q^{70} + 58 q^{71} + 12 q^{72} + 68 q^{73} + 18 q^{74} + 26 q^{75} - 8 q^{77} - 12 q^{78} + 68 q^{79} - 6 q^{80} + 20 q^{81} + 52 q^{82} - 10 q^{83} - 22 q^{84} - 24 q^{85} - 12 q^{86} + 14 q^{87} + 64 q^{88} + 38 q^{89} - 20 q^{90} + 28 q^{92} + 36 q^{93} + 24 q^{94} + 38 q^{96} - 72 q^{97} + 4 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{20} - 4 x^{19} - 23 x^{18} + 104 x^{17} + 205 x^{16} - 1126 x^{15} - 840 x^{14} + 6598 x^{13} + 1081 x^{12} - 22764 x^{11} + 3513 x^{10} + 47144 x^{9} - 15486 x^{8} - 57360 x^{7} + \cdots + 281 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( \nu \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( \nu^{2} - 3 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( - 914044996401 \nu^{19} + 1914472942731 \nu^{18} + 24503286232462 \nu^{17} - 46059892626710 \nu^{16} + \cdots + 111993463234130 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( 922157036717 \nu^{19} - 3407976013900 \nu^{18} - 21506930972301 \nu^{17} + 87310266587561 \nu^{16} + 196616081538516 \nu^{15} + \cdots + 834971263365987 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( - 936864479848 \nu^{19} + 1498480667218 \nu^{18} + 28174560025494 \nu^{17} - 39780350029698 \nu^{16} + \cdots + 12\!\cdots\!18 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( - 1146214698582 \nu^{19} + 2834286699437 \nu^{18} + 31025355710048 \nu^{17} - 72831761286760 \nu^{16} + \cdots + 326616373761577 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( 1221571262856 \nu^{19} - 3740070352842 \nu^{18} - 30930425745125 \nu^{17} + 96018055626976 \nu^{16} + \cdots + 188978806853413 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( - 1299561163989 \nu^{19} + 4012026932886 \nu^{18} + 33356823981022 \nu^{17} - 103647838871092 \nu^{16} + \cdots + 409564892267000 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( - 1405920375509 \nu^{19} + 3073929569321 \nu^{18} + 39341679877989 \nu^{17} - 79314920437965 \nu^{16} + \cdots + 314467427946152 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 1457526307000 \nu^{19} + 4530544064011 \nu^{18} + 37535131993886 \nu^{17} - 118225911946978 \nu^{16} + \cdots + 300000560748868 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( - 1457526307000 \nu^{19} + 4530544064011 \nu^{18} + 37535131993886 \nu^{17} - 118225911946978 \nu^{16} + \cdots + 300000560748868 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( - 1591742199164 \nu^{19} + 3562263337286 \nu^{18} + 44626140539646 \nu^{17} - 92292371628324 \nu^{16} + \cdots + 11\!\cdots\!19 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( - 99087022 \nu^{19} + 294850154 \nu^{18} + 2560021632 \nu^{17} - 7623532108 \nu^{16} - 27581503564 \nu^{15} + 81809322850 \nu^{14} + \cdots + 11596911783 ) / 785852939 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 101497934 \nu^{19} + 281020126 \nu^{18} + 2681518180 \nu^{17} - 7268664054 \nu^{16} - 29762663922 \nu^{15} + 78028159926 \nu^{14} + \cdots + 27843453182 ) / 785852939 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( - 122865697861 \nu^{19} + 296827104464 \nu^{18} + 3400228678335 \nu^{17} - 7747033366110 \nu^{16} - 40033862327063 \nu^{15} + \cdots + 90758374799234 ) / 876060584261 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( - 3186361197930 \nu^{19} + 10124714982758 \nu^{18} + 81098873797894 \nu^{17} - 262832597334184 \nu^{16} + \cdots + 518179844064736 ) / 16645151100959 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( - 172289456 \nu^{19} + 537484764 \nu^{18} + 4392943814 \nu^{17} - 13915008872 \nu^{16} - 46485996934 \nu^{15} + 149596232253 \nu^{14} + \cdots + 6269815895 ) / 785852939 \) Copy content Toggle raw display
\(\beta_{18}\)\(=\) \( ( 179968560 \nu^{19} - 468671842 \nu^{18} - 4851690550 \nu^{17} + 12143845744 \nu^{16} + 55259865755 \nu^{15} - 130553967583 \nu^{14} + \cdots - 81583886206 ) / 785852939 \) Copy content Toggle raw display
\(\beta_{19}\)\(=\) \( ( 4142034536298 \nu^{19} - 12317322896326 \nu^{18} - 107146972887326 \nu^{17} + 317360607922331 \nu^{16} + \cdots - 10\!\cdots\!68 ) / 16645151100959 \) Copy content Toggle raw display
\(\nu\)\(=\) \( \beta_1 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( \beta_{2} + 3 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( -\beta_{11} + \beta_{10} + 5\beta_1 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( \beta_{18} + \beta_{16} - \beta_{11} + \beta_{6} + \beta_{5} + 6\beta_{2} + \beta _1 + 15 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( - \beta_{19} - 2 \beta_{17} + \beta_{16} + \beta_{15} + \beta_{13} - 2 \beta_{12} - 9 \beta_{11} + 7 \beta_{10} + \beta_{9} - \beta_{8} - 2 \beta_{7} - \beta_{3} - \beta_{2} + 28 \beta _1 + 2 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( - 2 \beta_{19} + 9 \beta_{18} - 2 \beta_{17} + 10 \beta_{16} + 3 \beta_{14} - 3 \beta_{12} - 13 \beta_{11} + \beta_{9} - 2 \beta_{8} + 10 \beta_{6} + 10 \beta_{5} - \beta_{4} - 2 \beta_{3} + 32 \beta_{2} + 11 \beta _1 + 88 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( - 12 \beta_{19} + 2 \beta_{18} - 24 \beta_{17} + 15 \beta_{16} + 12 \beta_{15} + \beta_{14} + 13 \beta_{13} - 25 \beta_{12} - 72 \beta_{11} + 43 \beta_{10} + 13 \beta_{9} - 12 \beta_{8} - 22 \beta_{7} + 3 \beta_{5} - \beta_{4} - 12 \beta_{3} - 13 \beta_{2} + \cdots + 28 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( - 29 \beta_{19} + 67 \beta_{18} - 30 \beta_{17} + 81 \beta_{16} + 2 \beta_{15} + 41 \beta_{14} + 5 \beta_{13} - 45 \beta_{12} - 123 \beta_{11} + \beta_{10} + 16 \beta_{9} - 30 \beta_{8} + \beta_{7} + 77 \beta_{6} + 80 \beta_{5} - 13 \beta_{4} - 27 \beta_{3} + \cdots + 551 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( - 108 \beta_{19} + 31 \beta_{18} - 216 \beta_{17} + 154 \beta_{16} + 103 \beta_{15} + 23 \beta_{14} + 125 \beta_{13} - 232 \beta_{12} - 557 \beta_{11} + 264 \beta_{10} + 123 \beta_{9} - 107 \beta_{8} - 177 \beta_{7} + 2 \beta_{6} + \cdots + 280 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( - 294 \beta_{19} + 480 \beta_{18} - 318 \beta_{17} + 618 \beta_{16} + 34 \beta_{15} + 401 \beta_{14} + 96 \beta_{13} - 468 \beta_{12} - 1038 \beta_{11} + 20 \beta_{10} + 176 \beta_{9} - 308 \beta_{8} + 10 \beta_{7} + 544 \beta_{6} + \cdots + 3572 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( - 881 \beta_{19} + 338 \beta_{18} - 1766 \beta_{17} + 1364 \beta_{16} + 781 \beta_{15} + 315 \beta_{14} + 1090 \beta_{13} - 1929 \beta_{12} - 4227 \beta_{11} + 1660 \beta_{10} + 1035 \beta_{9} - 862 \beta_{8} + \cdots + 2478 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( - 2582 \beta_{19} + 3426 \beta_{18} - 2940 \beta_{17} + 4621 \beta_{16} + 380 \beta_{15} + 3466 \beta_{14} + 1207 \beta_{13} - 4191 \beta_{12} - 8310 \beta_{11} + 264 \beta_{10} + 1657 \beta_{9} - 2712 \beta_{8} + \cdots + 23701 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( - 6884 \beta_{19} + 3204 \beta_{18} - 13864 \beta_{17} + 11228 \beta_{16} + 5588 \beta_{15} + 3467 \beta_{14} + 9116 \beta_{13} - 15194 \beta_{12} - 31671 \beta_{11} + 10717 \beta_{10} + 8229 \beta_{9} + \cdots + 20680 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( - 21069 \beta_{19} + 24581 \beta_{18} - 25351 \beta_{17} + 34329 \beta_{16} + 3534 \beta_{15} + 28284 \beta_{14} + 12679 \beta_{13} - 34705 \beta_{12} - 64735 \beta_{11} + 2903 \beta_{10} + 14360 \beta_{9} + \cdots + 160038 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( - 52631 \beta_{19} + 28254 \beta_{18} - 106739 \beta_{17} + 88740 \beta_{16} + 38764 \beta_{15} + 33987 \beta_{14} + 74572 \beta_{13} - 116005 \beta_{12} - 235324 \beta_{11} + 70834 \beta_{10} + \cdots + 166940 \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( - 164813 \beta_{19} + 177573 \beta_{18} - 209913 \beta_{17} + 254652 \beta_{16} + 29639 \beta_{15} + 224012 \beta_{14} + 121018 \beta_{13} - 274362 \beta_{12} - 496643 \beta_{11} + \cdots + 1095734 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( - 397434 \beta_{19} + 238700 \beta_{18} - 813450 \beta_{17} + 684680 \beta_{16} + 263982 \beta_{15} + 310901 \beta_{14} + 601584 \beta_{13} - 868350 \beta_{12} - 1739485 \beta_{11} + \cdots + 1319557 \) Copy content Toggle raw display
\(\nu^{18}\)\(=\) \( - 1256328 \beta_{19} + 1290944 \beta_{18} - 1694219 \beta_{17} + 1889564 \beta_{16} + 232481 \beta_{15} + 1745077 \beta_{14} + 1090344 \beta_{13} - 2105574 \beta_{12} - 3775829 \beta_{11} + \cdots + 7587133 \) Copy content Toggle raw display
\(\nu^{19}\)\(=\) \( - 2978032 \beta_{19} + 1961346 \beta_{18} - 6164232 \beta_{17} + 5205430 \beta_{16} + 1775063 \beta_{15} + 2719494 \beta_{14} + 4805624 \beta_{13} - 6413694 \beta_{12} + \cdots + 10281057 \) Copy content Toggle raw display

Embeddings

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
−2.53431
−2.30325
−2.06847
−1.85752
−1.64623
−1.44794
−1.03012
−0.510520
−0.273748
−0.223281
0.913215
0.977871
1.21716
1.30420
1.53709
1.99921
2.17646
2.33995
2.68288
2.74734
−2.53431 1.00000 4.42270 0.282728 −2.53431 −1.00000 −6.13987 1.00000 −0.716520
1.2 −2.30325 1.00000 3.30497 2.19675 −2.30325 −1.00000 −3.00568 1.00000 −5.05967
1.3 −2.06847 1.00000 2.27857 −1.02727 −2.06847 −1.00000 −0.576212 1.00000 2.12488
1.4 −1.85752 1.00000 1.45038 2.04571 −1.85752 −1.00000 1.02093 1.00000 −3.79995
1.5 −1.64623 1.00000 0.710068 −2.20132 −1.64623 −1.00000 2.12352 1.00000 3.62387
1.6 −1.44794 1.00000 0.0965386 −1.66491 −1.44794 −1.00000 2.75610 1.00000 2.41069
1.7 −1.03012 1.00000 −0.938851 2.77661 −1.03012 −1.00000 3.02737 1.00000 −2.86024
1.8 −0.510520 1.00000 −1.73937 1.41361 −0.510520 −1.00000 1.90902 1.00000 −0.721675
1.9 −0.273748 1.00000 −1.92506 −1.72272 −0.273748 −1.00000 1.07448 1.00000 0.471591
1.10 −0.223281 1.00000 −1.95015 3.75914 −0.223281 −1.00000 0.881991 1.00000 −0.839343
1.11 0.913215 1.00000 −1.16604 −3.29422 0.913215 −1.00000 −2.89127 1.00000 −3.00833
1.12 0.977871 1.00000 −1.04377 −2.08291 0.977871 −1.00000 −2.97641 1.00000 −2.03681
1.13 1.21716 1.00000 −0.518514 4.41900 1.21716 −1.00000 −3.06544 1.00000 5.37864
1.14 1.30420 1.00000 −0.299053 0.149712 1.30420 −1.00000 −2.99843 1.00000 0.195255
1.15 1.53709 1.00000 0.362653 −1.29452 1.53709 −1.00000 −2.51675 1.00000 −1.98980
1.16 1.99921 1.00000 1.99685 −4.14471 1.99921 −1.00000 −0.00629798 1.00000 −8.28615
1.17 2.17646 1.00000 2.73697 −0.829735 2.17646 −1.00000 1.60400 1.00000 −1.80588
1.18 2.33995 1.00000 3.47537 2.96804 2.33995 −1.00000 3.45230 1.00000 6.94506
1.19 2.68288 1.00000 5.19785 −4.25250 2.68288 −1.00000 8.57946 1.00000 −11.4090
1.20 2.74734 1.00000 5.54787 0.503517 2.74734 −1.00000 9.74720 1.00000 1.38333
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.20
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(1\)
\(19\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 7581.2.a.bv yes 20
19.b odd 2 1 7581.2.a.bu 20
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7581.2.a.bu 20 19.b odd 2 1
7581.2.a.bv yes 20 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7581))\):

\( T_{2}^{20} - 4 T_{2}^{19} - 23 T_{2}^{18} + 104 T_{2}^{17} + 205 T_{2}^{16} - 1126 T_{2}^{15} - 840 T_{2}^{14} + 6598 T_{2}^{13} + 1081 T_{2}^{12} - 22764 T_{2}^{11} + 3513 T_{2}^{10} + 47144 T_{2}^{9} - 15486 T_{2}^{8} - 57360 T_{2}^{7} + \cdots + 281 \) Copy content Toggle raw display
\( T_{5}^{20} + 2 T_{5}^{19} - 61 T_{5}^{18} - 122 T_{5}^{17} + 1473 T_{5}^{16} + 2980 T_{5}^{15} - 18133 T_{5}^{14} - 37972 T_{5}^{13} + 121863 T_{5}^{12} + 273912 T_{5}^{11} - 438352 T_{5}^{10} - 1125524 T_{5}^{9} + \cdots + 15616 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{20} - 4 T^{19} - 23 T^{18} + 104 T^{17} + \cdots + 281 \) Copy content Toggle raw display
$3$ \( (T - 1)^{20} \) Copy content Toggle raw display
$5$ \( T^{20} + 2 T^{19} - 61 T^{18} + \cdots + 15616 \) Copy content Toggle raw display
$7$ \( (T + 1)^{20} \) Copy content Toggle raw display
$11$ \( T^{20} - 8 T^{19} - 86 T^{18} + \cdots - 963904 \) Copy content Toggle raw display
$13$ \( T^{20} - 151 T^{18} + \cdots - 13594624 \) Copy content Toggle raw display
$17$ \( T^{20} - 6 T^{19} - 145 T^{18} + \cdots + 54087680 \) Copy content Toggle raw display
$19$ \( T^{20} \) Copy content Toggle raw display
$23$ \( T^{20} + 4 T^{19} + \cdots + 30457144381 \) Copy content Toggle raw display
$29$ \( T^{20} - 14 T^{19} + \cdots - 3591845051120 \) Copy content Toggle raw display
$31$ \( T^{20} - 36 T^{19} + \cdots - 396299463424 \) Copy content Toggle raw display
$37$ \( T^{20} - 8 T^{19} + \cdots - 772111007744 \) Copy content Toggle raw display
$41$ \( T^{20} + \cdots - 387837618785024 \) Copy content Toggle raw display
$43$ \( T^{20} - 412 T^{18} + \cdots - 5704658902279 \) Copy content Toggle raw display
$47$ \( T^{20} + \cdots - 118055448018944 \) Copy content Toggle raw display
$53$ \( T^{20} - 22 T^{19} + \cdots - 32\!\cdots\!99 \) Copy content Toggle raw display
$59$ \( T^{20} - 44 T^{19} + \cdots - 16\!\cdots\!44 \) Copy content Toggle raw display
$61$ \( T^{20} + \cdots + 128538682246400 \) Copy content Toggle raw display
$67$ \( T^{20} - 52 T^{19} + \cdots + 11810578227401 \) Copy content Toggle raw display
$71$ \( T^{20} - 58 T^{19} + \cdots + 19\!\cdots\!76 \) Copy content Toggle raw display
$73$ \( T^{20} - 68 T^{19} + \cdots + 60\!\cdots\!16 \) Copy content Toggle raw display
$79$ \( T^{20} - 68 T^{19} + \cdots - 17428112496304 \) Copy content Toggle raw display
$83$ \( T^{20} + 10 T^{19} + \cdots + 17739489899776 \) Copy content Toggle raw display
$89$ \( T^{20} - 38 T^{19} + \cdots - 57\!\cdots\!20 \) Copy content Toggle raw display
$97$ \( T^{20} + 72 T^{19} + \cdots - 96\!\cdots\!44 \) Copy content Toggle raw display
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