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Properties

Label 805.2.r.b
Level $805$
Weight $2$
Character orbit 805.r
Analytic conductor $6.428$
Analytic rank $0$
Dimension $176$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [805,2,Mod(229,805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(805, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("805.229");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.r (of order \(6\), 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: \(6.42795736271\)
Analytic rank: \(0\)
Dimension: \(176\)
Relative dimension: \(88\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 176 q + 92 q^{4} - 96 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 176 q + 92 q^{4} - 96 q^{9} - 60 q^{16} + 108 q^{24} - 28 q^{25} - 48 q^{26} + 24 q^{29} + 12 q^{31} + 2 q^{35} - 48 q^{36} - 32 q^{39} - 46 q^{46} + 24 q^{49} + 20 q^{50} + 72 q^{54} - 132 q^{59} - 144 q^{64} + 46 q^{70} + 40 q^{71} + 66 q^{75} - 120 q^{81} - 180 q^{85} - 120 q^{94} + 40 q^{95} + 336 q^{96}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
229.1 −2.37629 − 1.37195i −0.277007 − 0.479791i 2.76451 + 4.78826i −1.24388 − 1.85816i 1.52016i 0.346712 + 2.62294i − 9.68327i 1.34653 − 2.33227i 0.406513 + 6.12207i
229.2 −2.37629 − 1.37195i −0.277007 − 0.479791i 2.76451 + 4.78826i 1.24388 + 1.85816i 1.52016i −0.346712 − 2.62294i − 9.68327i 1.34653 − 2.33227i −0.406513 − 6.12207i
229.3 −2.33902 − 1.35044i 1.52483 + 2.64107i 2.64735 + 4.58535i −1.20797 + 1.88171i − 8.23671i 2.60988 + 0.434182i − 8.89857i −3.15018 + 5.45628i 5.36658 − 2.77008i
229.4 −2.33902 − 1.35044i 1.52483 + 2.64107i 2.64735 + 4.58535i 1.20797 − 1.88171i − 8.23671i −2.60988 − 0.434182i − 8.89857i −3.15018 + 5.45628i −5.36658 + 2.77008i
229.5 −2.13029 − 1.22993i 0.697631 + 1.20833i 2.02544 + 3.50816i −1.79813 − 1.32918i − 3.43214i 2.16094 − 1.52655i − 5.04484i 0.526622 − 0.912135i 2.19576 + 5.04311i
229.6 −2.13029 − 1.22993i 0.697631 + 1.20833i 2.02544 + 3.50816i 1.79813 + 1.32918i − 3.43214i −2.16094 + 1.52655i − 5.04484i 0.526622 − 0.912135i −2.19576 − 5.04311i
229.7 −2.10195 − 1.21356i 0.157954 + 0.273584i 1.94547 + 3.36965i −1.95012 + 1.09409i − 0.766748i −1.54421 − 2.14835i − 4.58953i 1.45010 − 2.51165i 5.42680 + 0.0668735i
229.8 −2.10195 − 1.21356i 0.157954 + 0.273584i 1.94547 + 3.36965i 1.95012 − 1.09409i − 0.766748i 1.54421 + 2.14835i − 4.58953i 1.45010 − 2.51165i −5.42680 − 0.0668735i
229.9 −2.04383 − 1.18000i −1.14712 − 1.98688i 1.78482 + 3.09140i −0.952619 + 2.02300i 5.41445i −1.54159 + 2.15023i − 3.70435i −1.13179 + 1.96032i 4.33413 − 3.01056i
229.10 −2.04383 − 1.18000i −1.14712 − 1.98688i 1.78482 + 3.09140i 0.952619 − 2.02300i 5.41445i 1.54159 − 2.15023i − 3.70435i −1.13179 + 1.96032i −4.33413 + 3.01056i
229.11 −2.02925 − 1.17159i −0.952542 − 1.64985i 1.74525 + 3.02286i −1.89911 + 1.18042i 4.46396i 2.63288 − 0.260674i − 3.49251i −0.314672 + 0.545027i 5.23674 − 0.170391i
229.12 −2.02925 − 1.17159i −0.952542 − 1.64985i 1.74525 + 3.02286i 1.89911 − 1.18042i 4.46396i −2.63288 + 0.260674i − 3.49251i −0.314672 + 0.545027i −5.23674 + 0.170391i
229.13 −1.87149 − 1.08051i 0.688442 + 1.19242i 1.33498 + 2.31226i −0.316884 − 2.21350i − 2.97546i −1.31861 − 2.29374i − 1.44781i 0.552097 − 0.956259i −1.79865 + 4.48494i
229.14 −1.87149 − 1.08051i 0.688442 + 1.19242i 1.33498 + 2.31226i 0.316884 + 2.21350i − 2.97546i 1.31861 + 2.29374i − 1.44781i 0.552097 − 0.956259i 1.79865 − 4.48494i
229.15 −1.69669 − 0.979587i 1.25595 + 2.17537i 0.919180 + 1.59207i −2.03945 − 0.916864i − 4.92125i −0.600249 + 2.57676i 0.316679i −1.65482 + 2.86623i 2.56218 + 3.55346i
229.16 −1.69669 − 0.979587i 1.25595 + 2.17537i 0.919180 + 1.59207i 2.03945 + 0.916864i − 4.92125i 0.600249 − 2.57676i 0.316679i −1.65482 + 2.86623i −2.56218 − 3.55346i
229.17 −1.64018 − 0.946960i −1.66386 − 2.88190i 0.793468 + 1.37433i −1.41408 − 1.73216i 6.30246i 1.52207 + 2.16410i 0.782312i −4.03689 + 6.99210i 0.679063 + 4.18014i
229.18 −1.64018 − 0.946960i −1.66386 − 2.88190i 0.793468 + 1.37433i 1.41408 + 1.73216i 6.30246i −1.52207 − 2.16410i 0.782312i −4.03689 + 6.99210i −0.679063 − 4.18014i
229.19 −1.51909 − 0.877050i −0.304632 − 0.527638i 0.538432 + 0.932592i −1.54197 − 1.61936i 1.06871i −2.07561 − 1.64069i 1.61927i 1.31440 − 2.27661i 0.922134 + 3.81235i
229.20 −1.51909 − 0.877050i −0.304632 − 0.527638i 0.538432 + 0.932592i 1.54197 + 1.61936i 1.06871i 2.07561 + 1.64069i 1.61927i 1.31440 − 2.27661i −0.922134 − 3.81235i
See next 80 embeddings (of 176 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 229.88
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.d odd 6 1 inner
23.b odd 2 1 inner
35.i odd 6 1 inner
115.c odd 2 1 inner
161.g even 6 1 inner
805.r even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 805.2.r.b ✓ 176
5.b even 2 1 inner 805.2.r.b ✓ 176
7.d odd 6 1 inner 805.2.r.b ✓ 176
23.b odd 2 1 inner 805.2.r.b ✓ 176
35.i odd 6 1 inner 805.2.r.b ✓ 176
115.c odd 2 1 inner 805.2.r.b ✓ 176
161.g even 6 1 inner 805.2.r.b ✓ 176
805.r even 6 1 inner 805.2.r.b ✓ 176
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.r.b ✓ 176 1.a even 1 1 trivial
805.2.r.b ✓ 176 5.b even 2 1 inner
805.2.r.b ✓ 176 7.d odd 6 1 inner
805.2.r.b ✓ 176 23.b odd 2 1 inner
805.2.r.b ✓ 176 35.i odd 6 1 inner
805.2.r.b ✓ 176 115.c odd 2 1 inner
805.2.r.b ✓ 176 161.g even 6 1 inner
805.2.r.b ✓ 176 805.r even 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{88} - 67 T_{2}^{86} + 2409 T_{2}^{84} - 59898 T_{2}^{82} + 1141476 T_{2}^{80} - 17599212 T_{2}^{78} + \cdots + 11356900 \) acting on \(S_{2}^{\mathrm{new}}(805, [\chi])\). Copy content Toggle raw display