Properties

Label 806.2.g.g
Level $806$
Weight $2$
Character orbit 806.g
Analytic conductor $6.436$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [806,2,Mod(373,806)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(806, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("806.373");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 806 = 2 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 806.g (of order \(3\), degree \(2\), minimal)

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: no
Analytic conductor: \(6.43594240292\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 3 x^{19} + 29 x^{18} - 54 x^{17} + 432 x^{16} - 677 x^{15} + 4182 x^{14} - 4871 x^{13} + 27278 x^{12} - 27611 x^{11} + 125006 x^{10} - 99235 x^{9} + 376204 x^{8} + \cdots + 59049 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-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.

\(f(q)\) \(=\) \( q - \beta_{5} q^{2} + (\beta_{2} + \beta_1) q^{3} + (\beta_{5} - 1) q^{4} + \beta_{3} q^{5} - \beta_1 q^{6} + ( - \beta_{17} + \beta_{15}) q^{7} + q^{8} + (\beta_{15} - \beta_{11} + 2 \beta_{5} - \beta_1 - 2) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - \beta_{5} q^{2} + (\beta_{2} + \beta_1) q^{3} + (\beta_{5} - 1) q^{4} + \beta_{3} q^{5} - \beta_1 q^{6} + ( - \beta_{17} + \beta_{15}) q^{7} + q^{8} + (\beta_{15} - \beta_{11} + 2 \beta_{5} - \beta_1 - 2) q^{9} + (\beta_{17} - \beta_{3}) q^{10} - \beta_{16} q^{11} - \beta_{2} q^{12} + (\beta_{16} + \beta_{12} + \beta_{11} - \beta_{10} + \beta_{9} + \beta_{6} - \beta_{4} + \beta_{2} + 1) q^{13} + ( - \beta_{7} + \beta_{3}) q^{14} + (\beta_{19} + \beta_{18} + \beta_{17} - 2 \beta_{16} - \beta_{15} + \beta_{14} - \beta_{12} - \beta_{9} + \beta_{8} + \beta_{7} + \cdots - 1) q^{15}+ \cdots + (\beta_{14} - \beta_{13} + \beta_{10} - \beta_{9} - 2 \beta_{8} - \beta_{7} + \beta_{6} + 3 \beta_{4} - \beta_{3} + \cdots + 4) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 10 q^{2} - 3 q^{3} - 10 q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 20 q^{8} - 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 10 q^{2} - 3 q^{3} - 10 q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 20 q^{8} - 19 q^{9} - 3 q^{10} - 5 q^{11} + 6 q^{12} + 8 q^{13} + 2 q^{14} - 6 q^{15} - 10 q^{16} - 4 q^{17} + 38 q^{18} + 10 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} - 4 q^{23} - 3 q^{24} + 46 q^{25} - q^{26} + 36 q^{27} - q^{28} - 9 q^{29} - 6 q^{30} - 20 q^{31} - 10 q^{32} + 9 q^{33} + 8 q^{34} - 42 q^{35} - 19 q^{36} - 14 q^{37} - 20 q^{38} + 10 q^{39} + 6 q^{40} - 6 q^{41} - 2 q^{42} - 5 q^{43} + 10 q^{44} + 18 q^{45} - 4 q^{46} - 8 q^{47} - 3 q^{48} - 23 q^{49} - 23 q^{50} - 18 q^{51} - 7 q^{52} + 68 q^{53} - 18 q^{54} + 12 q^{55} - q^{56} + 46 q^{57} - 9 q^{58} - 10 q^{59} + 12 q^{60} - 30 q^{61} + 10 q^{62} - 35 q^{63} + 20 q^{64} - 6 q^{65} - 18 q^{66} + 4 q^{67} - 4 q^{68} + 21 q^{69} + 84 q^{70} - 3 q^{71} - 19 q^{72} - 12 q^{73} - 14 q^{74} + 5 q^{75} + 10 q^{76} - 62 q^{77} - 14 q^{78} + 22 q^{79} - 3 q^{80} - 10 q^{81} - 6 q^{82} + 94 q^{83} - 2 q^{84} - 25 q^{85} + 10 q^{86} - 34 q^{87} - 5 q^{88} + 4 q^{89} - 36 q^{90} + 40 q^{91} + 8 q^{92} + 3 q^{93} + 4 q^{94} - q^{95} + 6 q^{96} + 50 q^{97} - 23 q^{98} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{20} - 3 x^{19} + 29 x^{18} - 54 x^{17} + 432 x^{16} - 677 x^{15} + 4182 x^{14} - 4871 x^{13} + 27278 x^{12} - 27611 x^{11} + 125006 x^{10} - 99235 x^{9} + 376204 x^{8} + \cdots + 59049 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( \nu \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( - 21\!\cdots\!82 \nu^{19} + \cdots - 80\!\cdots\!59 ) / 25\!\cdots\!65 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( - 43\!\cdots\!57 \nu^{19} + \cdots + 18\!\cdots\!16 ) / 30\!\cdots\!20 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( 68\!\cdots\!53 \nu^{19} + \cdots + 28\!\cdots\!16 ) / 15\!\cdots\!10 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( - 11\!\cdots\!71 \nu^{19} + \cdots + 24\!\cdots\!43 ) / 21\!\cdots\!65 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( - 89\!\cdots\!37 \nu^{19} + \cdots - 13\!\cdots\!24 ) / 15\!\cdots\!10 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( 10\!\cdots\!87 \nu^{19} + \cdots + 11\!\cdots\!24 ) / 15\!\cdots\!10 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( 21\!\cdots\!99 \nu^{19} + \cdots + 17\!\cdots\!28 ) / 30\!\cdots\!20 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( - 70\!\cdots\!27 \nu^{19} + \cdots + 50\!\cdots\!44 ) / 49\!\cdots\!84 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 22\!\cdots\!51 \nu^{19} + \cdots - 30\!\cdots\!52 ) / 12\!\cdots\!10 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 25\!\cdots\!21 \nu^{19} + \cdots - 12\!\cdots\!33 ) / 12\!\cdots\!10 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( 23\!\cdots\!73 \nu^{19} + \cdots + 43\!\cdots\!31 ) / 82\!\cdots\!40 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 20\!\cdots\!64 \nu^{19} + \cdots - 34\!\cdots\!47 ) / 61\!\cdots\!55 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( 20\!\cdots\!34 \nu^{19} + \cdots + 15\!\cdots\!03 ) / 61\!\cdots\!55 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( 60\!\cdots\!77 \nu^{19} + \cdots - 10\!\cdots\!61 ) / 12\!\cdots\!10 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( - 13\!\cdots\!44 \nu^{19} + \cdots + 18\!\cdots\!97 ) / 24\!\cdots\!20 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( 13\!\cdots\!11 \nu^{19} + \cdots - 12\!\cdots\!23 ) / 24\!\cdots\!20 \) Copy content Toggle raw display
\(\beta_{18}\)\(=\) \( ( - 13\!\cdots\!87 \nu^{19} + \cdots + 18\!\cdots\!41 ) / 24\!\cdots\!20 \) Copy content Toggle raw display
\(\beta_{19}\)\(=\) \( ( - 87\!\cdots\!83 \nu^{19} + \cdots + 99\!\cdots\!94 ) / 12\!\cdots\!10 \) Copy content Toggle raw display
\(\nu\)\(=\) \( \beta_1 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( -\beta_{15} + \beta_{11} + \beta_{7} - 5\beta_{5} - \beta_{4} + \beta_{2} + \beta_1 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( \beta_{10} - \beta_{9} + \beta_{7} - \beta_{6} - \beta_{4} - \beta_{3} + 7\beta_{2} - 2 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( - \beta_{18} - 2 \beta_{17} + \beta_{16} + 10 \beta_{15} + \beta_{14} - \beta_{13} + 2 \beta_{12} - 10 \beta_{11} + \beta_{9} + 3 \beta_{6} + 36 \beta_{5} - \beta_{4} + 3 \beta_{2} - 13 \beta _1 - 34 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( - 4 \beta_{19} - \beta_{18} - 16 \beta_{17} - 10 \beta_{16} + 15 \beta_{15} - 3 \beta_{14} + 3 \beta_{13} + 3 \beta_{12} - 27 \beta_{11} + 3 \beta_{10} + 3 \beta_{9} - \beta_{8} - 15 \beta_{7} + \beta_{6} + 35 \beta_{5} + 27 \beta_{4} + 16 \beta_{3} - 71 \beta_{2} - 68 \beta _1 + 3 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( - 16 \beta_{16} - 38 \beta_{14} + 38 \beta_{13} - 16 \beta_{12} - 16 \beta_{11} + 13 \beta_{10} + 3 \beta_{9} - 19 \beta_{8} - 100 \beta_{7} - 62 \beta_{6} + 127 \beta_{4} + 42 \beta_{3} - 213 \beta_{2} + 279 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( 79 \beta_{19} + 28 \beta_{18} + 213 \beta_{17} + 22 \beta_{16} - 199 \beta_{15} - 55 \beta_{14} + 66 \beta_{13} - 121 \beta_{12} + 246 \beta_{11} - 88 \beta_{10} + 22 \beta_{9} - 99 \beta_{6} - 441 \beta_{5} - 22 \beta_{4} - 99 \beta_{2} + \cdots + 320 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( 238 \beta_{19} + 253 \beta_{18} + 624 \beta_{17} - 63 \beta_{16} - 1027 \beta_{15} + 336 \beta_{14} - 207 \beta_{13} - 336 \beta_{12} + 1060 \beta_{11} - 207 \beta_{10} - 336 \beta_{9} + 253 \beta_{8} + 1027 \beta_{7} - 31 \beta_{6} + \cdots - 336 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( 751 \beta_{16} + 1776 \beta_{14} - 1776 \beta_{13} + 751 \beta_{12} + 751 \beta_{11} + 40 \beta_{10} - 791 \beta_{9} + 480 \beta_{8} + 2459 \beta_{7} + 1632 \beta_{6} - 3428 \beta_{4} - 2626 \beta_{3} + 8454 \beta_{2} + \cdots - 4298 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( - 3599 \beta_{19} - 3001 \beta_{18} - 8104 \beta_{17} + 3430 \beta_{16} + 10784 \beta_{15} + 2514 \beta_{14} - 4455 \beta_{13} + 6969 \beta_{12} - 8083 \beta_{11} + 1025 \beta_{10} + 3430 \beta_{9} + 10399 \beta_{6} + \cdots - 17200 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( - 14379 \beta_{19} - 6761 \beta_{18} - 31041 \beta_{17} - 2857 \beta_{16} + 29087 \beta_{15} - 13857 \beta_{14} + 9210 \beta_{13} + 13857 \beta_{12} - 33414 \beta_{11} + 9210 \beta_{10} + 13857 \beta_{9} + \cdots + 13857 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( - 29592 \beta_{16} - 84679 \beta_{14} + 84679 \beta_{13} - 29592 \beta_{12} - 29592 \beta_{11} + 15762 \beta_{10} + 13830 \beta_{9} - 34012 \beta_{8} - 115116 \beta_{7} - 108280 \beta_{6} + \cdots + 204655 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( 173426 \beta_{19} + 86263 \beta_{18} + 357866 \beta_{17} - 99219 \beta_{16} - 335006 \beta_{15} - 107391 \beta_{14} + 174319 \beta_{13} - 281710 \beta_{12} + 241534 \beta_{11} - 75100 \beta_{10} + \cdots + 326513 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( 578064 \beta_{19} + 378101 \beta_{18} + 1154648 \beta_{17} - 140048 \beta_{16} - 1242816 \beta_{15} + 654957 \beta_{14} - 341429 \beta_{13} - 654957 \beta_{12} + 1115950 \beta_{11} + \cdots - 654957 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( 1219720 \beta_{16} + 3320900 \beta_{14} - 3320900 \beta_{13} + 1219720 \beta_{12} + 1219720 \beta_{11} - 436374 \beta_{10} - 783346 \beta_{9} + 1041083 \beta_{8} + 3795200 \beta_{7} + \cdots - 5378790 \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( - 6800005 \beta_{19} - 4168391 \beta_{18} - 13238430 \beta_{17} + 5517102 \beta_{16} + 13516764 \beta_{15} + 3884770 \beta_{14} - 7602365 \beta_{13} + 11487135 \beta_{12} + \cdots - 12597782 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( - 23291322 \beta_{19} - 12152449 \beta_{18} - 45644470 \beta_{17} + 2586935 \beta_{16} + 42550114 \beta_{15} - 24642168 \beta_{14} + 13655795 \beta_{13} + 24642168 \beta_{12} + \cdots + 24642168 \) Copy content Toggle raw display
\(\nu^{18}\)\(=\) \( - 43761948 \beta_{16} - 130639834 \beta_{14} + 130639834 \beta_{13} - 43761948 \beta_{12} - 43761948 \beta_{11} + 19359944 \beta_{10} + 24402004 \beta_{9} + \cdots + 208208321 \) Copy content Toggle raw display
\(\nu^{19}\)\(=\) \( 264030713 \beta_{19} + 138930878 \beta_{18} + 509493805 \beta_{17} - 192156979 \beta_{16} - 473887733 \beta_{15} - 151667617 \beta_{14} + 283716663 \beta_{13} + \cdots + 340827305 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/806\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1 + \beta_{5}\) \(1\)

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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
373.1
1.65755 + 2.87096i
1.44311 + 2.49953i
1.32972 + 2.30315i
0.719197 + 1.24569i
0.428084 + 0.741463i
0.213190 + 0.369257i
−0.655189 1.13482i
−0.998125 1.72880i
−1.28693 2.22903i
−1.35061 2.33932i
1.65755 2.87096i
1.44311 2.49953i
1.32972 2.30315i
0.719197 1.24569i
0.428084 0.741463i
0.213190 0.369257i
−0.655189 + 1.13482i
−0.998125 + 1.72880i
−1.28693 + 2.22903i
−1.35061 + 2.33932i
−0.500000 + 0.866025i −1.65755 + 2.87096i −0.500000 0.866025i 2.86158 −1.65755 2.87096i −1.93688 3.35478i 1.00000 −3.99496 6.91947i −1.43079 + 2.47820i
373.2 −0.500000 + 0.866025i −1.44311 + 2.49953i −0.500000 0.866025i 0.331062 −1.44311 2.49953i 0.599602 + 1.03854i 1.00000 −2.66511 4.61610i −0.165531 + 0.286708i
373.3 −0.500000 + 0.866025i −1.32972 + 2.30315i −0.500000 0.866025i −3.64678 −1.32972 2.30315i 0.174014 + 0.301402i 1.00000 −2.03632 3.52702i 1.82339 3.15821i
373.4 −0.500000 + 0.866025i −0.719197 + 1.24569i −0.500000 0.866025i 1.25876 −0.719197 1.24569i −1.33582 2.31371i 1.00000 0.465511 + 0.806288i −0.629379 + 1.09012i
373.5 −0.500000 + 0.866025i −0.428084 + 0.741463i −0.500000 0.866025i −2.23921 −0.428084 0.741463i 2.58272 + 4.47340i 1.00000 1.13349 + 1.96326i 1.11960 1.93921i
373.6 −0.500000 + 0.866025i −0.213190 + 0.369257i −0.500000 0.866025i 3.56549 −0.213190 0.369257i 1.19888 + 2.07652i 1.00000 1.40910 + 2.44063i −1.78274 + 3.08780i
373.7 −0.500000 + 0.866025i 0.655189 1.13482i −0.500000 0.866025i 3.87429 0.655189 + 1.13482i −1.72219 2.98292i 1.00000 0.641455 + 1.11103i −1.93714 + 3.35523i
373.8 −0.500000 + 0.866025i 0.998125 1.72880i −0.500000 0.866025i 1.17900 0.998125 + 1.72880i 0.361697 + 0.626478i 1.00000 −0.492509 0.853050i −0.589498 + 1.02104i
373.9 −0.500000 + 0.866025i 1.28693 2.22903i −0.500000 0.866025i −0.229603 1.28693 + 2.22903i −1.94749 3.37315i 1.00000 −1.81238 3.13913i 0.114802 0.198842i
373.10 −0.500000 + 0.866025i 1.35061 2.33932i −0.500000 0.866025i −3.95458 1.35061 + 2.33932i 1.52547 + 2.64219i 1.00000 −2.14828 3.72093i 1.97729 3.42476i
497.1 −0.500000 0.866025i −1.65755 2.87096i −0.500000 + 0.866025i 2.86158 −1.65755 + 2.87096i −1.93688 + 3.35478i 1.00000 −3.99496 + 6.91947i −1.43079 2.47820i
497.2 −0.500000 0.866025i −1.44311 2.49953i −0.500000 + 0.866025i 0.331062 −1.44311 + 2.49953i 0.599602 1.03854i 1.00000 −2.66511 + 4.61610i −0.165531 0.286708i
497.3 −0.500000 0.866025i −1.32972 2.30315i −0.500000 + 0.866025i −3.64678 −1.32972 + 2.30315i 0.174014 0.301402i 1.00000 −2.03632 + 3.52702i 1.82339 + 3.15821i
497.4 −0.500000 0.866025i −0.719197 1.24569i −0.500000 + 0.866025i 1.25876 −0.719197 + 1.24569i −1.33582 + 2.31371i 1.00000 0.465511 0.806288i −0.629379 1.09012i
497.5 −0.500000 0.866025i −0.428084 0.741463i −0.500000 + 0.866025i −2.23921 −0.428084 + 0.741463i 2.58272 4.47340i 1.00000 1.13349 1.96326i 1.11960 + 1.93921i
497.6 −0.500000 0.866025i −0.213190 0.369257i −0.500000 + 0.866025i 3.56549 −0.213190 + 0.369257i 1.19888 2.07652i 1.00000 1.40910 2.44063i −1.78274 3.08780i
497.7 −0.500000 0.866025i 0.655189 + 1.13482i −0.500000 + 0.866025i 3.87429 0.655189 1.13482i −1.72219 + 2.98292i 1.00000 0.641455 1.11103i −1.93714 3.35523i
497.8 −0.500000 0.866025i 0.998125 + 1.72880i −0.500000 + 0.866025i 1.17900 0.998125 1.72880i 0.361697 0.626478i 1.00000 −0.492509 + 0.853050i −0.589498 1.02104i
497.9 −0.500000 0.866025i 1.28693 + 2.22903i −0.500000 + 0.866025i −0.229603 1.28693 2.22903i −1.94749 + 3.37315i 1.00000 −1.81238 + 3.13913i 0.114802 + 0.198842i
497.10 −0.500000 0.866025i 1.35061 + 2.33932i −0.500000 + 0.866025i −3.95458 1.35061 2.33932i 1.52547 2.64219i 1.00000 −2.14828 + 3.72093i 1.97729 + 3.42476i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 373.10
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 806.2.g.g 20
13.c even 3 1 inner 806.2.g.g 20
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
806.2.g.g 20 1.a even 1 1 trivial
806.2.g.g 20 13.c even 3 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(806, [\chi])\):

\( T_{3}^{20} + 3 T_{3}^{19} + 29 T_{3}^{18} + 54 T_{3}^{17} + 432 T_{3}^{16} + 677 T_{3}^{15} + 4182 T_{3}^{14} + 4871 T_{3}^{13} + 27278 T_{3}^{12} + 27611 T_{3}^{11} + 125006 T_{3}^{10} + 99235 T_{3}^{9} + 376204 T_{3}^{8} + \cdots + 59049 \) Copy content Toggle raw display
\( T_{5}^{10} - 3 T_{5}^{9} - 32 T_{5}^{8} + 102 T_{5}^{7} + 288 T_{5}^{6} - 1057 T_{5}^{5} - 362 T_{5}^{4} + 3072 T_{5}^{3} - 2160 T_{5}^{2} - 32 T_{5} + 144 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T^{2} + T + 1)^{10} \) Copy content Toggle raw display
$3$ \( T^{20} + 3 T^{19} + 29 T^{18} + \cdots + 59049 \) Copy content Toggle raw display
$5$ \( (T^{10} - 3 T^{9} - 32 T^{8} + 102 T^{7} + \cdots + 144)^{2} \) Copy content Toggle raw display
$7$ \( T^{20} + T^{19} + 47 T^{18} + \cdots + 2509056 \) Copy content Toggle raw display
$11$ \( T^{20} + 5 T^{19} + 73 T^{18} + \cdots + 50168889 \) Copy content Toggle raw display
$13$ \( T^{20} - 8 T^{19} + \cdots + 137858491849 \) Copy content Toggle raw display
$17$ \( T^{20} + 4 T^{19} + 105 T^{18} + \cdots + 429981696 \) Copy content Toggle raw display
$19$ \( T^{20} - 10 T^{19} + \cdots + 30964737024 \) Copy content Toggle raw display
$23$ \( T^{20} + 4 T^{19} + \cdots + 3830124544 \) Copy content Toggle raw display
$29$ \( T^{20} + 9 T^{19} + \cdots + 26598733500816 \) Copy content Toggle raw display
$31$ \( (T + 1)^{20} \) Copy content Toggle raw display
$37$ \( T^{20} + 14 T^{19} + \cdots + 21983696361 \) Copy content Toggle raw display
$41$ \( T^{20} + 6 T^{19} + \cdots + 473623369209 \) Copy content Toggle raw display
$43$ \( T^{20} + \cdots + 112170043553296 \) Copy content Toggle raw display
$47$ \( (T^{10} + 4 T^{9} - 128 T^{8} - 555 T^{7} + \cdots - 10609)^{2} \) Copy content Toggle raw display
$53$ \( (T^{10} - 34 T^{9} + 348 T^{8} + \cdots - 1423656)^{2} \) Copy content Toggle raw display
$59$ \( T^{20} + 10 T^{19} + \cdots + 463793688576 \) Copy content Toggle raw display
$61$ \( T^{20} + 30 T^{19} + \cdots + 62\!\cdots\!76 \) Copy content Toggle raw display
$67$ \( T^{20} - 4 T^{19} + \cdots + 32195728560384 \) Copy content Toggle raw display
$71$ \( T^{20} + 3 T^{19} + 247 T^{18} + \cdots + 483516121 \) Copy content Toggle raw display
$73$ \( (T^{10} + 6 T^{9} - 457 T^{8} + \cdots - 66717184)^{2} \) Copy content Toggle raw display
$79$ \( (T^{10} - 11 T^{9} - 351 T^{8} + \cdots + 11160224)^{2} \) Copy content Toggle raw display
$83$ \( (T^{10} - 47 T^{9} + 755 T^{8} + \cdots - 3568212)^{2} \) Copy content Toggle raw display
$89$ \( T^{20} - 4 T^{19} + \cdots + 10\!\cdots\!76 \) Copy content Toggle raw display
$97$ \( T^{20} - 50 T^{19} + \cdots + 18283483294561 \) Copy content Toggle raw display
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