↑

Properties

Label 805.2.u.d
Level $805$
Weight $2$
Character orbit 805.u
Analytic conductor $6.428$
Analytic rank $0$
Dimension $130$
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: \(130\)
Relative dimension: \(13\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 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 −1.53322 − 1.76943i −1.38891 − 0.892597i −0.495486 + 3.44618i 0.415415 − 0.909632i 0.550112 + 3.82611i 0.959493 + 0.281733i 2.91822 − 1.87543i −0.113909 − 0.249426i −2.24645 + 0.659617i
36.2 −1.47427 − 1.70140i −0.576050 − 0.370205i −0.436652 + 3.03698i 0.415415 − 0.909632i 0.219387 + 1.52587i 0.959493 + 0.281733i 2.02307 − 1.30015i −1.05146 − 2.30238i −2.16008 + 0.634256i
36.3 −1.26899 − 1.46449i 1.73669 + 1.11610i −0.249772 + 1.73720i 0.415415 − 0.909632i −0.569318 − 3.95969i 0.959493 + 0.281733i −0.399286 + 0.256605i 0.524163 + 1.14776i −1.85930 + 0.545941i
36.4 −0.438445 − 0.505992i 0.0821184 + 0.0527743i 0.220835 − 1.53594i 0.415415 − 0.909632i −0.00930099 − 0.0646898i 0.959493 + 0.281733i −2.00048 + 1.28563i −1.24229 − 2.72023i −0.642403 + 0.188627i
36.5 −0.382224 − 0.441110i −1.87858 − 1.20729i 0.236147 − 1.64244i 0.415415 − 0.909632i 0.185490 + 1.29011i 0.959493 + 0.281733i −1.79679 + 1.15473i 0.825261 + 1.80707i −0.560029 + 0.164439i
36.6 −0.250829 − 0.289473i 1.59098 + 1.02246i 0.263751 − 1.83443i 0.415415 − 0.909632i −0.103090 − 0.717009i 0.959493 + 0.281733i −1.24162 + 0.797940i 0.239547 + 0.524536i −0.367512 + 0.107911i
36.7 −0.104891 − 0.121051i −2.72566 − 1.75168i 0.280979 − 1.95425i 0.415415 − 0.909632i 0.0738558 + 0.513678i 0.959493 + 0.281733i −0.535527 + 0.344162i 3.11462 + 6.82007i −0.153685 + 0.0451259i
36.8 0.290736 + 0.335528i −0.0197965 − 0.0127225i 0.256579 − 1.78454i 0.415415 − 0.909632i −0.00148684 − 0.0103412i 0.959493 + 0.281733i 1.42034 − 0.912795i −1.24601 − 2.72839i 0.425983 − 0.125080i
36.9 0.677819 + 0.782245i 2.49523 + 1.60359i 0.132161 − 0.919203i 0.415415 − 0.909632i 0.436917 + 3.03882i 0.959493 + 0.281733i 2.55012 − 1.63886i 2.40844 + 5.27376i 0.993131 − 0.291609i
36.10 1.13848 + 1.31387i −2.68348 − 1.72457i −0.145502 + 1.01199i 0.415415 − 0.909632i −0.789218 − 5.48913i 0.959493 + 0.281733i 1.42977 − 0.918859i 2.98068 + 6.52678i 1.66808 − 0.489793i
36.11 1.24199 + 1.43333i 1.46429 + 0.941042i −0.227273 + 1.58072i 0.415415 − 0.909632i 0.469806 + 3.26757i 0.959493 + 0.281733i 0.643026 − 0.413248i 0.0123391 + 0.0270189i 1.81974 − 0.534325i
36.12 1.39788 + 1.61324i −0.946197 − 0.608084i −0.363842 + 2.53058i 0.415415 − 0.909632i −0.341685 − 2.37647i 0.959493 + 0.281733i −0.999516 + 0.642350i −0.720722 − 1.57816i 2.04815 − 0.601392i
36.13 1.80777 + 2.08628i 1.16685 + 0.749889i −0.799893 + 5.56338i 0.415415 − 0.909632i 0.544920 + 3.79000i 0.959493 + 0.281733i −8.40814 + 5.40358i −0.447039 − 0.978878i 2.64872 − 0.777734i
71.1 −2.37136 − 1.52398i 0.249488 + 1.73522i 2.47000 + 5.40855i −0.959493 − 0.281733i 2.05282 − 4.49506i 0.654861 − 0.755750i 1.58294 − 11.0096i −0.0702814 + 0.0206365i 1.84595 + 2.13034i
71.2 −1.90133 − 1.22191i −0.232141 − 1.61458i 1.29116 + 2.82724i −0.959493 − 0.281733i −1.53149 + 3.35350i 0.654861 − 0.755750i 0.356423 − 2.47898i 0.325509 − 0.0955781i 1.48006 + 1.70808i
71.3 −1.56407 − 1.00517i 0.0329436 + 0.229128i 0.605124 + 1.32504i −0.959493 − 0.281733i 0.178785 − 0.391485i 0.654861 − 0.755750i −0.143761 + 0.999879i 2.82706 − 0.830101i 1.21753 + 1.40510i
71.4 −1.28289 − 0.824465i −0.438498 − 3.04982i 0.135242 + 0.296138i −0.959493 − 0.281733i −1.95193 + 4.27412i 0.654861 − 0.755750i −0.363399 + 2.52750i −6.23065 + 1.82948i 0.998648 + 1.15250i
71.5 −0.937084 − 0.602227i 0.379948 + 2.64260i −0.315382 − 0.690589i −0.959493 − 0.281733i 1.23540 − 2.70515i 0.654861 − 0.755750i −0.437406 + 3.04222i −3.96049 + 1.16291i 0.729458 + 0.841840i
71.6 −0.366295 − 0.235403i 0.126863 + 0.882351i −0.752073 − 1.64681i −0.959493 − 0.281733i 0.161239 − 0.353064i 0.654861 − 0.755750i −0.236116 + 1.64222i 2.11603 − 0.621322i 0.285136 + 0.329065i
71.7 0.575812 + 0.370052i −0.202015 − 1.40505i −0.636209 − 1.39310i −0.959493 − 0.281733i 0.403617 − 0.883798i 0.654861 − 0.755750i 0.344004 − 2.39260i 0.945137 − 0.277517i −0.448232 − 0.517288i
See next 80 embeddings (of 130 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 36.13
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.d ✓ 130
23.c even 11 1 inner 805.2.u.d ✓ 130
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.u.d ✓ 130 1.a even 1 1 trivial
805.2.u.d ✓ 130 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{130} - 2 T_{2}^{129} + 23 T_{2}^{128} - 29 T_{2}^{127} + 253 T_{2}^{126} - 213 T_{2}^{125} + \cdots + 279841 \) acting on \(S_{2}^{\mathrm{new}}(805, [\chi])\). Copy content Toggle raw display