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Properties

Label 805.2.bi.a
Level $805$
Weight $2$
Character orbit 805.bi
Analytic conductor $6.428$
Analytic rank $0$
Dimension $1440$
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(43,805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(805, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([33, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("805.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.bi (of order \(44\), degree \(20\), 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: \(1440\)
Relative dimension: \(72\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1440 q - 8 q^{3} + 16 q^{6}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 1440 q - 8 q^{3} + 16 q^{6} - 32 q^{12} + 16 q^{13} + 192 q^{16} - 72 q^{18} - 36 q^{23} + 8 q^{25} - 8 q^{27} + 40 q^{32} - 44 q^{33} - 208 q^{36} - 88 q^{37} - 32 q^{41} + 80 q^{46} - 192 q^{47} - 24 q^{48} + 56 q^{50} + 64 q^{52} - 56 q^{55} - 88 q^{57} + 24 q^{62} - 352 q^{66} + 16 q^{70} - 344 q^{71} + 48 q^{72} - 32 q^{73} - 144 q^{75} - 352 q^{76} - 40 q^{78} - 16 q^{81} + 96 q^{82} - 16 q^{85} + 16 q^{87} - 836 q^{90} - 112 q^{92} + 8 q^{93} - 56 q^{95} - 96 q^{96} + 132 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
43.1 −2.23045 − 1.66970i 1.59141 − 0.593565i 1.62357 + 5.52938i 1.61243 − 1.54922i −4.54064 − 1.33325i −0.977147 − 0.212565i 3.66374 − 9.82286i −0.0869839 + 0.0753720i −6.18317 + 0.763194i
43.2 −2.16533 − 1.62095i 1.67938 − 0.626377i 1.49773 + 5.10078i −1.86513 − 1.23341i −4.65174 − 1.36588i 0.977147 + 0.212565i 3.13454 − 8.40403i 0.160730 − 0.139273i 2.03934 + 5.69401i
43.3 −2.15556 − 1.61363i −0.0690759 + 0.0257640i 1.47916 + 5.03756i −0.299327 + 2.21594i 0.190471 + 0.0559273i 0.977147 + 0.212565i 3.05839 − 8.19987i −2.26314 + 1.96102i 4.22093 − 4.29359i
43.4 −2.09427 − 1.56775i −1.67772 + 0.625756i 1.36467 + 4.64762i −1.62977 + 1.53097i 4.49463 + 1.31974i −0.977147 − 0.212565i 2.59990 − 6.97060i 0.155916 − 0.135102i 5.81336 − 0.651188i
43.5 −2.02354 − 1.51480i 2.86191 − 1.06744i 1.23661 + 4.21152i 0.167422 + 2.22979i −7.40814 − 2.17523i −0.977147 − 0.212565i 2.11059 − 5.65871i 4.78387 − 4.14525i 3.03890 − 4.76567i
43.6 −1.96451 − 1.47062i −1.89325 + 0.706146i 1.13314 + 3.85911i 0.839987 − 2.07230i 4.75779 + 1.39701i −0.977147 − 0.212565i 1.73405 − 4.64917i 0.818505 − 0.709238i −4.69772 + 2.83576i
43.7 −1.94022 − 1.45243i −2.92735 + 1.09185i 1.09143 + 3.71706i 1.82592 + 1.29074i 7.26552 + 2.13335i 0.977147 + 0.212565i 1.58721 − 4.25547i 5.11002 − 4.42786i −1.66797 − 5.15633i
43.8 −1.79192 − 1.34142i 0.806322 − 0.300743i 0.848121 + 2.88843i −0.763442 − 2.10170i −1.84829 − 0.542706i −0.977147 − 0.212565i 0.790352 − 2.11902i −1.70754 + 1.47959i −1.45123 + 4.79018i
43.9 −1.72569 − 1.29184i 0.322608 − 0.120327i 0.745709 + 2.53965i −2.22560 + 0.216142i −0.712165 − 0.209111i −0.977147 − 0.212565i 0.487304 − 1.30651i −2.17765 + 1.88695i 4.11992 + 2.50212i
43.10 −1.69521 − 1.26902i 2.43947 − 0.909877i 0.699862 + 2.38351i −1.69071 + 1.46339i −5.29007 − 1.55330i 0.977147 + 0.212565i 0.358269 − 0.960556i 2.85591 − 2.47466i 4.72317 − 0.335221i
43.11 −1.68532 − 1.26162i −2.03123 + 0.757611i 0.685172 + 2.33348i 2.16810 + 0.547133i 4.37910 + 1.28582i −0.977147 − 0.212565i 0.317820 − 0.852109i 1.28469 − 1.11319i −2.96367 − 3.65741i
43.12 −1.68322 − 1.26004i 2.98148 − 1.11203i 0.682050 + 2.32285i 0.518670 − 2.17508i −6.41968 − 1.88499i 0.977147 + 0.212565i 0.309280 − 0.829212i 5.38535 − 4.66643i −3.61372 + 3.00759i
43.13 −1.67478 − 1.25372i 0.494482 − 0.184432i 0.669592 + 2.28042i 2.09659 − 0.777381i −1.05937 − 0.311060i 0.977147 + 0.212565i 0.275401 − 0.738378i −2.05675 + 1.78219i −4.48593 − 1.32660i
43.14 −1.58315 − 1.18513i −0.824652 + 0.307579i 0.538359 + 1.83348i −0.0541008 − 2.23541i 1.67007 + 0.490376i 0.977147 + 0.212565i −0.0615870 + 0.165121i −1.68180 + 1.45729i −2.56360 + 3.60310i
43.15 −1.48688 − 1.11306i −1.02325 + 0.381654i 0.408432 + 1.39099i 0.0244033 + 2.23593i 1.94626 + 0.571473i 0.977147 + 0.212565i −0.357176 + 0.957626i −1.36586 + 1.18352i 2.45245 − 3.35172i
43.16 −1.39904 − 1.04731i −0.608807 + 0.227073i 0.296997 + 1.01148i −2.23575 − 0.0376414i 1.08956 + 0.319925i 0.977147 + 0.212565i −0.577641 + 1.54871i −1.94817 + 1.68809i 3.08849 + 2.39419i
43.17 −1.35083 − 1.01122i −2.75020 + 1.02577i 0.238712 + 0.812979i −1.12025 + 1.93521i 4.75232 + 1.39541i −0.977147 − 0.212565i −0.679728 + 1.82242i 4.24413 − 3.67756i 3.47018 − 1.48133i
43.18 −1.29203 − 0.967204i 2.14863 − 0.801398i 0.170401 + 0.580334i 2.23604 − 0.0111527i −3.55122 − 1.04273i −0.977147 − 0.212565i −0.786898 + 2.10976i 1.70712 − 1.47923i −2.89983 − 2.14830i
43.19 −1.24670 − 0.933271i −2.97965 + 1.11135i 0.119811 + 0.408040i −0.325229 − 2.21229i 4.75194 + 1.39530i 0.977147 + 0.212565i −0.857017 + 2.29775i 5.37598 − 4.65832i −1.65920 + 3.06160i
43.20 −1.21877 − 0.912362i 1.44268 − 0.538092i 0.0895383 + 0.304939i −0.0652285 + 2.23512i −2.24923 − 0.660435i −0.977147 − 0.212565i −0.894986 + 2.39955i −0.475467 + 0.411995i 2.11873 − 2.66459i
See next 80 embeddings (of 1440 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 43.72
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
23.d odd 22 1 inner
115.l even 44 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 805.2.bi.a ✓ 1440
5.c odd 4 1 inner 805.2.bi.a ✓ 1440
23.d odd 22 1 inner 805.2.bi.a ✓ 1440
115.l even 44 1 inner 805.2.bi.a ✓ 1440
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.bi.a ✓ 1440 1.a even 1 1 trivial
805.2.bi.a ✓ 1440 5.c odd 4 1 inner
805.2.bi.a ✓ 1440 23.d odd 22 1 inner
805.2.bi.a ✓ 1440 115.l even 44 1 inner

Hecke kernels

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