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Properties

Label 184.3.g.a
Level $184$
Weight $3$
Character orbit 184.g
Analytic conductor $5.014$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [184,3,Mod(139,184)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(184, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("184.139");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 184.g (of order \(2\), degree \(1\), 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: \(5.01363686423\)
Analytic rank: \(0\)
Dimension: \(44\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 3 q^{6} + 15 q^{8} + 132 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q - 3 q^{6} + 15 q^{8} + 132 q^{9} + 26 q^{10} - 19 q^{12} - 8 q^{14} - 16 q^{16} - 8 q^{17} - 57 q^{18} + 40 q^{20} + 44 q^{22} - 88 q^{24} - 244 q^{25} + 19 q^{26} - 48 q^{27} + 6 q^{28} + 86 q^{30} + 160 q^{32} + 16 q^{33} + 18 q^{34} + 96 q^{35} + 179 q^{36} - 156 q^{38} + 130 q^{40} + 88 q^{41} + 100 q^{42} - 128 q^{43} - 158 q^{44} + 5 q^{48} - 340 q^{49} + 4 q^{50} + 160 q^{51} - 127 q^{52} + 53 q^{54} - 6 q^{56} - 176 q^{57} + 147 q^{58} + 16 q^{59} - 283 q^{62} - 405 q^{64} + 96 q^{65} - 602 q^{66} - 288 q^{67} + 72 q^{68} + 312 q^{70} - 57 q^{72} + 280 q^{73} - 198 q^{74} + 160 q^{75} + 172 q^{76} - 185 q^{78} - 90 q^{80} + 284 q^{81} - 75 q^{82} - 480 q^{83} - 254 q^{84} - 98 q^{86} + 204 q^{88} - 200 q^{89} + 488 q^{90} + 192 q^{91} + 19 q^{94} - 107 q^{96} + 184 q^{97} + 200 q^{98} + 256 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
139.1 −1.97298 − 0.327653i 2.30854 3.78529 + 1.29291i − 6.63468i −4.55469 − 0.756400i − 5.68430i −7.04466 − 3.79114i −3.67066 −2.17387 + 13.0901i
139.2 −1.97298 + 0.327653i 2.30854 3.78529 − 1.29291i 6.63468i −4.55469 + 0.756400i 5.68430i −7.04466 + 3.79114i −3.67066 −2.17387 − 13.0901i
139.3 −1.85711 − 0.742392i −5.73355 2.89771 + 2.75740i 7.99646i 10.6478 + 4.25654i 1.47255i −3.33429 − 7.27204i 23.8736 5.93650 − 14.8503i
139.4 −1.85711 + 0.742392i −5.73355 2.89771 − 2.75740i − 7.99646i 10.6478 − 4.25654i − 1.47255i −3.33429 + 7.27204i 23.8736 5.93650 + 14.8503i
139.5 −1.75284 − 0.963097i 5.65315 2.14489 + 3.37631i − 0.736380i −9.90906 − 5.44453i 11.2523i −0.507935 − 7.98386i 22.9581 −0.709206 + 1.29076i
139.6 −1.75284 + 0.963097i 5.65315 2.14489 − 3.37631i 0.736380i −9.90906 + 5.44453i − 11.2523i −0.507935 + 7.98386i 22.9581 −0.709206 − 1.29076i
139.7 −1.75201 − 0.964609i −2.68155 2.13906 + 3.38000i − 5.82129i 4.69809 + 2.58664i 9.89299i −0.487268 − 7.98515i −1.80931 −5.61527 + 10.1990i
139.8 −1.75201 + 0.964609i −2.68155 2.13906 − 3.38000i 5.82129i 4.69809 − 2.58664i − 9.89299i −0.487268 + 7.98515i −1.80931 −5.61527 − 10.1990i
139.9 −1.66789 − 1.10369i 2.74812 1.56374 + 3.68167i 5.36507i −4.58357 − 3.03307i − 10.3195i 1.45526 − 7.86652i −1.44785 5.92137 − 8.94837i
139.10 −1.66789 + 1.10369i 2.74812 1.56374 − 3.68167i − 5.36507i −4.58357 + 3.03307i 10.3195i 1.45526 + 7.86652i −1.44785 5.92137 + 8.94837i
139.11 −1.54512 − 1.26989i 0.245976 0.774772 + 3.92425i 4.88516i −0.380062 − 0.312362i 0.635668i 3.78624 − 7.04730i −8.93950 6.20360 − 7.54814i
139.12 −1.54512 + 1.26989i 0.245976 0.774772 − 3.92425i − 4.88516i −0.380062 + 0.312362i − 0.635668i 3.78624 + 7.04730i −8.93950 6.20360 + 7.54814i
139.13 −1.17096 − 1.62137i −3.75579 −1.25770 + 3.79713i − 6.41150i 4.39789 + 6.08953i − 13.5423i 7.62928 − 2.40710i 5.10596 −10.3954 + 7.50762i
139.14 −1.17096 + 1.62137i −3.75579 −1.25770 − 3.79713i 6.41150i 4.39789 − 6.08953i 13.5423i 7.62928 + 2.40710i 5.10596 −10.3954 − 7.50762i
139.15 −1.02925 − 1.71483i −2.92203 −1.88130 + 3.52997i 1.54046i 3.00749 + 5.01079i 1.69513i 7.98963 − 0.407108i −0.461746 2.64163 − 1.58551i
139.16 −1.02925 + 1.71483i −2.92203 −1.88130 − 3.52997i − 1.54046i 3.00749 − 5.01079i − 1.69513i 7.98963 + 0.407108i −0.461746 2.64163 + 1.58551i
139.17 −0.688422 − 1.87778i 3.83484 −3.05215 + 2.58542i − 4.53003i −2.63999 − 7.20100i − 5.30399i 6.95602 + 3.95142i 5.70598 −8.50642 + 3.11857i
139.18 −0.688422 + 1.87778i 3.83484 −3.05215 − 2.58542i 4.53003i −2.63999 + 7.20100i 5.30399i 6.95602 − 3.95142i 5.70598 −8.50642 − 3.11857i
139.19 −0.541272 − 1.92536i 1.17721 −3.41405 + 2.08429i 1.54173i −0.637193 − 2.26656i 8.23215i 5.86095 + 5.44512i −7.61417 2.96839 − 0.834497i
139.20 −0.541272 + 1.92536i 1.17721 −3.41405 − 2.08429i − 1.54173i −0.637193 + 2.26656i − 8.23215i 5.86095 − 5.44512i −7.61417 2.96839 + 0.834497i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 139.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 184.3.g.a ✓ 44
4.b odd 2 1 736.3.g.a 44
8.b even 2 1 736.3.g.a 44
8.d odd 2 1 inner 184.3.g.a ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
184.3.g.a ✓ 44 1.a even 1 1 trivial
184.3.g.a ✓ 44 8.d odd 2 1 inner
736.3.g.a 44 4.b odd 2 1
736.3.g.a 44 8.b even 2 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(184, [\chi])\).