↑

Properties

Label 805.2.u.b
Level $805$
Weight $2$
Character orbit 805.u
Analytic conductor $6.428$
Analytic rank $0$
Dimension $110$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [805,2,Mod(36,805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(805, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("805.36");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.u (of order \(11\), degree \(10\), 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: \(6.42795736271\)
Analytic rank: \(0\)
Dimension: \(110\)
Relative dimension: \(11\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 110 q + 4 q^{2} + 2 q^{3} - 2 q^{4} - 11 q^{5} + 9 q^{6} - 11 q^{7} - q^{8} - 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 110 q + 4 q^{2} + 2 q^{3} - 2 q^{4} - 11 q^{5} + 9 q^{6} - 11 q^{7} - q^{8} - 21 q^{9} + 4 q^{10} + 14 q^{11} + 23 q^{12} + 3 q^{13} + 4 q^{14} + 2 q^{15} - 86 q^{16} - 35 q^{17} + 47 q^{18} + 7 q^{19} - 2 q^{20} + 2 q^{21} - 62 q^{22} + 8 q^{23} - 152 q^{24} - 11 q^{25} + 29 q^{26} + 26 q^{27} - 13 q^{28} + 23 q^{29} + 9 q^{30} - 16 q^{31} + 34 q^{32} + 6 q^{33} + 29 q^{34} - 11 q^{35} - 160 q^{36} + 52 q^{37} + 32 q^{38} + 6 q^{39} - 45 q^{40} + 22 q^{41} + 9 q^{42} + 14 q^{43} + 57 q^{44} + 78 q^{45} - 154 q^{46} + 6 q^{47} + 56 q^{48} - 11 q^{49} - 7 q^{50} + 34 q^{51} + 73 q^{52} + 22 q^{53} - 202 q^{54} - 19 q^{55} + 21 q^{56} + 79 q^{57} - 3 q^{58} + 10 q^{59} + 12 q^{60} + 24 q^{61} - 146 q^{62} + q^{63} + 33 q^{64} + 14 q^{65} + 134 q^{66} + 66 q^{67} + 74 q^{68} + 36 q^{69} + 4 q^{70} + 72 q^{71} + 121 q^{72} - 36 q^{73} - 50 q^{74} + 2 q^{75} + 84 q^{76} - 19 q^{77} - 196 q^{78} - 18 q^{79} + 13 q^{80} - 35 q^{81} - 163 q^{82} - 33 q^{83} - 54 q^{84} + 9 q^{85} + 58 q^{86} + 29 q^{87} + 185 q^{88} - 17 q^{89} - 52 q^{90} - 30 q^{91} + 68 q^{92} - 38 q^{93} + 129 q^{94} + 18 q^{95} - 215 q^{96} - 20 q^{97} - 7 q^{98} + 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
36.1 −1.82569 − 2.10696i −2.59980 − 1.67079i −0.821505 + 5.71369i 0.415415 − 0.909632i 1.22614 + 8.52802i −0.959493 − 0.281733i 8.84767 − 5.68605i 2.72116 + 5.95852i −2.67498 + 0.785445i
36.2 −1.16169 − 1.34067i 0.718037 + 0.461454i −0.163223 + 1.13524i 0.415415 − 0.909632i −0.215483 − 1.49872i −0.959493 − 0.281733i −1.27310 + 0.818170i −0.943608 − 2.06621i −1.70210 + 0.499781i
36.3 −1.15610 − 1.33421i 1.52153 + 0.977826i −0.158923 + 1.10534i 0.415415 − 0.909632i −0.454413 − 3.16051i −0.959493 − 0.281733i −1.31184 + 0.843070i 0.112655 + 0.246679i −1.69391 + 0.497376i
36.4 −0.965445 − 1.11418i −2.28089 − 1.46584i −0.0246896 + 0.171720i 0.415415 − 0.909632i 0.568860 + 3.95651i −0.959493 − 0.281733i −2.26531 + 1.45583i 1.80753 + 3.95793i −1.41456 + 0.415351i
36.5 −0.380442 − 0.439053i −0.528899 − 0.339903i 0.236598 − 1.64557i 0.415415 − 0.909632i 0.0519799 + 0.361528i −0.959493 − 0.281733i −1.78996 + 1.15034i −1.08204 − 2.36935i −0.557418 + 0.163673i
36.6 0.273404 + 0.315525i 1.50560 + 0.967590i 0.259823 − 1.80711i 0.415415 − 0.909632i 0.106338 + 0.739596i −0.959493 − 0.281733i 1.34367 − 0.863524i 0.0843529 + 0.184707i 0.400587 − 0.117623i
36.7 0.568880 + 0.656522i −0.952663 − 0.612240i 0.177232 − 1.23268i 0.415415 − 0.909632i −0.140002 − 0.973736i −0.959493 − 0.281733i 2.37170 − 1.52420i −0.713515 − 1.56238i 0.833515 − 0.244742i
36.8 0.737151 + 0.850717i 1.13472 + 0.729239i 0.104301 − 0.725429i 0.415415 − 0.909632i 0.216082 + 1.50288i −0.959493 − 0.281733i 2.58795 − 1.66318i −0.490449 − 1.07393i 1.08006 − 0.317135i
36.9 1.48095 + 1.70910i −0.896960 − 0.576441i −0.443202 + 3.08253i 0.415415 − 0.909632i −0.343152 − 2.38668i −0.959493 − 0.281733i −2.11979 + 1.36231i −0.773992 − 1.69481i 2.16986 − 0.637129i
36.10 1.59505 + 1.84079i 2.39842 + 1.54137i −0.559680 + 3.89266i 0.415415 − 0.909632i 0.988268 + 6.87355i −0.959493 − 0.281733i −3.96018 + 2.54506i 2.13035 + 4.66482i 2.33705 − 0.686219i
36.11 1.74936 + 2.01887i −1.70160 − 1.09355i −0.730941 + 5.08381i 0.415415 − 0.909632i −0.768973 − 5.34832i −0.959493 − 0.281733i −7.04766 + 4.52926i 0.453342 + 0.992681i 2.56314 − 0.752605i
71.1 −2.29433 − 1.47448i −0.368843 − 2.56536i 2.25905 + 4.94663i −0.959493 − 0.281733i −2.93632 + 6.42963i −0.654861 + 0.755750i 1.33442 − 9.28109i −3.56653 + 1.04723i 1.78599 + 2.06114i
71.2 −1.99144 − 1.27982i 0.419874 + 2.92029i 1.49706 + 3.27810i −0.959493 − 0.281733i 2.90129 − 6.35294i −0.654861 + 0.755750i 0.540297 − 3.75785i −5.47331 + 1.60711i 1.55020 + 1.78903i
71.3 −1.92659 − 1.23814i −0.0715105 − 0.497367i 1.34791 + 2.95151i −0.959493 − 0.281733i −0.478039 + 1.04676i −0.654861 + 0.755750i 0.405682 − 2.82158i 2.63622 − 0.774064i 1.49972 + 1.73077i
71.4 −0.973402 − 0.625568i −0.0221389 − 0.153979i −0.274653 − 0.601406i −0.959493 − 0.281733i −0.0747745 + 0.163733i −0.654861 + 0.755750i −0.438213 + 3.04784i 2.85526 − 0.838380i 0.757730 + 0.874467i
71.5 −0.417030 − 0.268009i −0.301037 − 2.09376i −0.728745 − 1.59573i −0.959493 − 0.281733i −0.435603 + 0.953838i −0.654861 + 0.755750i −0.264859 + 1.84213i −1.41471 + 0.415396i 0.324630 + 0.374643i
71.6 −0.212249 − 0.136404i 0.321393 + 2.23533i −0.804387 − 1.76136i −0.959493 − 0.281733i 0.236693 − 0.518286i −0.654861 + 0.755750i −0.141339 + 0.983033i −2.01495 + 0.591643i 0.165222 + 0.190676i
71.7 0.467373 + 0.300362i 0.200067 + 1.39149i −0.702610 − 1.53850i −0.959493 − 0.281733i −0.324447 + 0.710439i −0.654861 + 0.755750i 0.291858 − 2.02992i 0.982249 − 0.288414i −0.363819 − 0.419870i
71.8 1.15027 + 0.739234i −0.345045 − 2.39984i −0.0541747 − 0.118626i −0.959493 − 0.281733i 1.37715 − 3.01553i −0.654861 + 0.755750i 0.414559 − 2.88332i −2.76170 + 0.810907i −0.895410 − 1.03336i
71.9 1.67415 + 1.07591i −0.0311645 − 0.216754i 0.814354 + 1.78319i −0.959493 − 0.281733i 0.181033 − 0.396408i −0.654861 + 0.755750i 0.0112324 − 0.0781233i 2.83247 − 0.831688i −1.30321 − 1.50399i
See next 80 embeddings (of 110 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 36.11
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 805.2.u.b ✓ 110
23.c even 11 1 inner 805.2.u.b ✓ 110
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.u.b ✓ 110 1.a even 1 1 trivial
805.2.u.b ✓ 110 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{110} - 4 T_{2}^{109} + 20 T_{2}^{108} - 49 T_{2}^{107} + 236 T_{2}^{106} - 654 T_{2}^{105} + \cdots + 38631509401 \) acting on \(S_{2}^{\mathrm{new}}(805, [\chi])\). Copy content Toggle raw display