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Properties

Label 805.2.be.a
Level $805$
Weight $2$
Character orbit 805.be
Analytic conductor $6.428$
Analytic rank $0$
Dimension $720$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [805,2,Mod(29,805)]
 
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([11, 0, 18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("805.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.be (of order \(22\), 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: \(720\)
Relative dimension: \(72\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 720 q + 80 q^{4} + 4 q^{5} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 720 q + 80 q^{4} + 4 q^{5} - 8 q^{6} + 64 q^{9} + 16 q^{11} - 8 q^{14} - 18 q^{15} - 96 q^{16} - 36 q^{20} + 8 q^{21} + 24 q^{24} - 30 q^{25} + 40 q^{26} - 8 q^{29} - 44 q^{30} - 8 q^{31} + 12 q^{34} + 4 q^{35} - 72 q^{36} - 72 q^{39} - 20 q^{40} - 16 q^{41} - 148 q^{44} + 32 q^{45} - 32 q^{46} + 72 q^{49} + 32 q^{50} - 248 q^{54} - 88 q^{55} - 72 q^{59} - 200 q^{60} - 40 q^{61} - 20 q^{65} + 128 q^{66} - 208 q^{69} - 8 q^{70} + 188 q^{71} - 128 q^{74} + 132 q^{75} - 44 q^{76} - 40 q^{79} - 180 q^{80} - 264 q^{81} - 24 q^{84} - 4 q^{85} - 376 q^{86} + 48 q^{89} + 394 q^{90} - 160 q^{91} + 144 q^{94} + 64 q^{95} - 732 q^{96} - 88 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
29.1 −2.52275 − 1.15210i −0.531347 + 1.80960i 3.72719 + 4.30141i 0.723345 + 2.11584i 3.42530 − 3.95300i −0.989821 − 0.142315i −2.88441 − 9.82340i −0.468569 − 0.301131i 0.612841 − 6.17109i
29.2 −2.47773 − 1.13154i 0.786821 − 2.67967i 3.54905 + 4.09582i 1.87741 − 1.21463i −4.98169 + 5.74917i −0.989821 − 0.142315i −2.62418 − 8.93714i −4.03776 − 2.59491i −6.02613 + 0.885148i
29.3 −2.43601 − 1.11249i −0.952304 + 3.24325i 3.38681 + 3.90858i −0.156920 − 2.23056i 5.92791 − 6.84117i 0.989821 + 0.142315i −2.39307 − 8.15006i −7.08803 − 4.55520i −2.09921 + 5.60823i
29.4 −2.38751 − 1.09034i 0.362133 − 1.23331i 3.20163 + 3.69487i 1.91740 + 1.15047i −2.20932 + 2.54969i 0.989821 + 0.142315i −2.13632 − 7.27564i 1.13384 + 0.728677i −3.32339 − 4.83737i
29.5 −2.35644 − 1.07615i −0.257650 + 0.877474i 3.08500 + 3.56029i −2.19304 + 0.436570i 1.55143 − 1.79045i 0.989821 + 0.142315i −1.97855 − 6.73832i 1.82018 + 1.16976i 5.63758 + 1.33129i
29.6 −2.27102 − 1.03714i 0.199769 − 0.680349i 2.77216 + 3.19925i 0.232125 − 2.22399i −1.15930 + 1.33790i 0.989821 + 0.142315i −1.57081 − 5.34968i 2.10079 + 1.35010i −2.83375 + 4.80998i
29.7 −2.22193 − 1.01472i 0.753806 − 2.56723i 2.59760 + 2.99779i −1.05342 + 1.97239i −4.27993 + 4.93930i −0.989821 − 0.142315i −1.35340 − 4.60926i −3.49867 − 2.24846i 4.34205 − 3.31358i
29.8 −2.22163 − 1.01459i 0.250850 − 0.854318i 2.59655 + 2.99658i −2.22975 + 0.168024i −1.42408 + 1.64347i −0.989821 − 0.142315i −1.35212 − 4.60491i 1.85683 + 1.19331i 5.12416 + 1.88898i
29.9 −2.17014 − 0.991068i −0.449930 + 1.53232i 2.41755 + 2.79001i 1.98240 − 1.03444i 2.49504 − 2.87943i −0.989821 − 0.142315i −1.13706 − 3.87247i 0.378189 + 0.243047i −5.32729 + 0.280188i
29.10 −2.06247 − 0.941900i 0.844138 − 2.87487i 2.05690 + 2.37379i −1.87108 − 1.22436i −4.44885 + 5.13425i 0.989821 + 0.142315i −0.728846 − 2.48222i −5.02855 − 3.23166i 2.70582 + 4.28759i
29.11 −2.02855 − 0.926409i −0.707671 + 2.41011i 1.94707 + 2.24704i −2.19193 − 0.442093i 3.66829 − 4.23344i −0.989821 − 0.142315i −0.611485 − 2.08253i −2.78406 − 1.78920i 4.03688 + 2.92743i
29.12 −1.84732 − 0.843643i 0.397906 − 1.35514i 1.39114 + 1.60546i −1.29868 − 1.82028i −1.87832 + 2.16770i −0.989821 − 0.142315i −0.0711338 − 0.242259i 0.845673 + 0.543481i 0.863420 + 4.45827i
29.13 −1.79028 − 0.817596i 0.241372 − 0.822039i 1.22694 + 1.41596i 2.04956 + 0.894049i −1.10422 + 1.27434i −0.989821 − 0.142315i 0.0700971 + 0.238729i 1.90627 + 1.22509i −2.93832 − 3.27631i
29.14 −1.77545 − 0.810823i −0.848268 + 2.88894i 1.18508 + 1.36766i 1.82997 + 1.28499i 3.84848 − 4.44138i 0.989821 + 0.142315i 0.104662 + 0.356447i −5.10264 − 3.27927i −2.20713 − 3.76522i
29.15 −1.74286 − 0.795940i −0.146151 + 0.497746i 1.09434 + 1.26293i 1.87688 − 1.21546i 0.650898 − 0.751176i 0.989821 + 0.142315i 0.177543 + 0.604655i 2.29737 + 1.47643i −4.23857 + 0.624495i
29.16 −1.72360 − 0.787141i −0.893659 + 3.04352i 1.04148 + 1.20193i −0.562738 + 2.16410i 3.93599 − 4.54238i −0.989821 − 0.142315i 0.218668 + 0.744713i −5.94064 − 3.81782i 2.67339 − 3.28708i
29.17 −1.68094 − 0.767659i −0.561823 + 1.91339i 0.926532 + 1.06927i −1.50063 + 1.65775i 2.41322 − 2.78501i 0.989821 + 0.142315i 0.304641 + 1.03751i −0.821670 − 0.528055i 3.79504 − 1.63460i
29.18 −1.44358 − 0.659259i −0.465275 + 1.58458i 0.339565 + 0.391879i −0.677391 − 2.13100i 1.71631 − 1.98072i −0.989821 − 0.142315i 0.662374 + 2.25584i 0.229349 + 0.147394i −0.427012 + 3.52283i
29.19 −1.40208 − 0.640306i 0.0945030 − 0.321848i 0.246102 + 0.284017i −0.500514 + 2.17933i −0.338581 + 0.390744i 0.989821 + 0.142315i 0.705310 + 2.40207i 2.42911 + 1.56109i 2.09720 − 2.73511i
29.20 −1.40024 − 0.639466i 0.409784 − 1.39560i 0.242021 + 0.279307i 0.809486 − 2.08440i −1.46623 + 1.69212i −0.989821 − 0.142315i 0.707087 + 2.40812i 0.743996 + 0.478137i −2.46637 + 2.40102i
See next 80 embeddings (of 720 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 29.72
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
23.c even 11 1 inner
115.j even 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 805.2.be.a ✓ 720
5.b even 2 1 inner 805.2.be.a ✓ 720
23.c even 11 1 inner 805.2.be.a ✓ 720
115.j even 22 1 inner 805.2.be.a ✓ 720
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.be.a ✓ 720 1.a even 1 1 trivial
805.2.be.a ✓ 720 5.b even 2 1 inner
805.2.be.a ✓ 720 23.c even 11 1 inner
805.2.be.a ✓ 720 115.j even 22 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(805, [\chi])\).