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Properties

Label 184.2.j.a
Level $184$
Weight $2$
Character orbit 184.j
Analytic conductor $1.469$
Analytic rank $0$
Dimension $220$
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] = [184,2,Mod(11,184)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(184, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("184.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 184.j (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: \(1.46924739719\)
Analytic rank: \(0\)
Dimension: \(220\)
Relative dimension: \(22\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 220 q - 11 q^{2} - 18 q^{3} - 3 q^{4} - 12 q^{6} - 8 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 220 q - 11 q^{2} - 18 q^{3} - 3 q^{4} - 12 q^{6} - 8 q^{8} - 36 q^{9} - 11 q^{10} - 22 q^{11} - 6 q^{12} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 6 q^{18} - 22 q^{19} - 11 q^{20} - 18 q^{24} - 32 q^{25} - 10 q^{26} - 18 q^{27} - 11 q^{28} - 11 q^{30} - 11 q^{32} - 22 q^{33} + 11 q^{34} + 2 q^{35} - 41 q^{36} + 44 q^{38} - 99 q^{40} - 18 q^{41} + 99 q^{42} - 22 q^{43} - 88 q^{44} + 45 q^{46} - 100 q^{48} - 28 q^{49} + 14 q^{50} - 22 q^{51} - 118 q^{52} + 102 q^{54} - 66 q^{56} - 22 q^{57} + 43 q^{58} - 6 q^{59} - 33 q^{60} - 56 q^{62} + 18 q^{64} - 22 q^{65} + 22 q^{66} - 22 q^{67} - 10 q^{70} - 23 q^{72} - 18 q^{73} + 14 q^{75} + 44 q^{76} + 98 q^{78} + 88 q^{80} + 4 q^{81} + 14 q^{82} - 22 q^{83} + 143 q^{84} + 99 q^{86} + 77 q^{88} - 22 q^{89} + 176 q^{90} + 36 q^{92} + 111 q^{94} + 101 q^{96} - 22 q^{97} + 121 q^{98} - 22 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1 −1.41156 + 0.0866089i 0.0849297 − 0.590699i 1.98500 − 0.244507i −1.48124 + 0.434930i −0.0687235 + 0.841162i 1.80365 + 2.08153i −2.78077 + 0.517055i 2.53677 + 0.744862i 2.05318 − 0.742218i
11.2 −1.36036 + 0.386548i 0.402816 − 2.80165i 1.70116 − 1.05169i 3.83602 − 1.12636i 0.534997 + 3.96696i −0.00464829 − 0.00536442i −1.90766 + 2.08826i −4.80850 − 1.41190i −4.78298 + 3.01506i
11.3 −1.32635 − 0.490713i −0.271373 + 1.88744i 1.51840 + 1.30171i 1.80873 − 0.531090i 1.28613 − 2.37024i −0.0734431 − 0.0847579i −1.37516 − 2.47162i −0.610307 − 0.179202i −2.65962 − 0.183154i
11.4 −1.29360 + 0.571497i −0.353914 + 2.46153i 1.34678 − 1.47857i −2.85901 + 0.839481i −0.948934 − 3.38648i −2.82277 − 3.25765i −0.897191 + 2.68236i −3.05539 − 0.897142i 3.21864 − 2.71986i
11.5 −1.22528 − 0.706185i 0.204278 − 1.42078i 1.00261 + 1.73054i −0.226441 + 0.0664891i −1.25363 + 1.59660i −2.97374 − 3.43188i −0.00638677 − 2.82842i 0.901582 + 0.264728i 0.324407 + 0.0784417i
11.6 −1.05723 + 0.939288i −0.353914 + 2.46153i 0.235476 − 1.98609i 2.85901 − 0.839481i −1.93791 − 2.93483i 2.82277 + 3.25765i 1.61656 + 2.32094i −3.05539 − 0.897142i −2.23412 + 3.57296i
11.7 −0.916731 + 1.07685i 0.402816 − 2.80165i −0.319209 − 1.97436i −3.83602 + 1.12636i 2.64768 + 3.00213i 0.00464829 + 0.00536442i 2.41872 + 1.46622i −4.80850 − 1.41190i 2.30368 − 5.16339i
11.8 −0.730057 − 1.21120i 0.00352593 − 0.0245234i −0.934035 + 1.76850i −3.56863 + 1.04785i −0.0322770 + 0.0136328i 1.35535 + 1.56416i 2.82391 − 0.159795i 2.87789 + 0.845025i 3.87446 + 3.55736i
11.9 −0.665165 + 1.24802i 0.0849297 − 0.590699i −1.11511 − 1.66028i 1.48124 − 0.434930i 0.680712 + 0.498906i −1.80365 − 2.08153i 2.81380 − 0.287322i 2.53677 + 0.744862i −0.442465 + 2.13792i
11.10 −0.232723 − 1.39493i −0.166341 + 1.15693i −1.89168 + 0.649268i 2.24350 − 0.658750i 1.65255 − 0.0372094i 0.445092 + 0.513663i 1.34592 + 2.48767i 1.56767 + 0.460310i −1.44103 − 2.97622i
11.11 −0.168317 − 1.40416i 0.394507 − 2.74385i −1.94334 + 0.472688i 0.121643 − 0.0357177i −3.91922 − 0.0921141i −0.745341 − 0.860169i 0.990827 + 2.64920i −4.49462 − 1.31974i −0.0706280 − 0.164795i
11.12 −0.104617 + 1.41034i −0.271373 + 1.88744i −1.97811 − 0.295092i −1.80873 + 0.531090i −2.63354 − 0.580187i 0.0734431 + 0.0847579i 0.623124 − 2.75893i −0.610307 − 0.179202i −0.559793 − 2.60648i
11.13 0.133370 + 1.40791i 0.204278 − 1.42078i −1.96442 + 0.375546i 0.226441 − 0.0664891i 2.02758 + 0.0981153i 2.97374 + 3.43188i −0.790730 − 2.71565i 0.901582 + 0.264728i 0.123811 + 0.309941i
11.14 0.592390 − 1.28416i −0.468808 + 3.26063i −1.29815 − 1.52145i −2.28389 + 0.670610i 3.90947 + 2.53359i 2.41865 + 2.79127i −2.72280 + 0.765741i −7.53346 − 2.21202i −0.491780 + 3.33015i
11.15 0.798474 + 1.16724i 0.00352593 − 0.0245234i −0.724878 + 1.86402i 3.56863 − 1.04785i 0.0314399 − 0.0154657i −1.35535 − 1.56416i −2.75454 + 0.642265i 2.87789 + 0.845025i 4.07254 + 3.32876i
11.16 0.805898 − 1.16212i 0.249165 − 1.73298i −0.701056 − 1.87310i 1.27762 − 0.375142i −1.81313 − 1.68616i 1.98083 + 2.28600i −2.74176 − 0.694820i −0.0626488 − 0.0183953i 0.593668 − 1.78707i
11.17 0.890428 − 1.09870i −0.119292 + 0.829693i −0.414274 − 1.95662i 1.57873 − 0.463558i 0.805361 + 0.869848i −1.68916 − 1.94939i −2.51862 − 1.28707i 2.20432 + 0.647247i 0.896439 − 2.14732i
11.18 1.17220 + 0.791169i −0.166341 + 1.15693i 0.748103 + 1.85482i −2.24350 + 0.658750i −1.11031 + 1.22454i −0.445092 − 0.513663i −0.590547 + 2.76609i 1.56767 + 0.460310i −3.15101 − 1.00280i
11.19 1.20735 + 0.736416i 0.394507 − 2.74385i 0.915382 + 1.77822i −0.121643 + 0.0357177i 2.49693 − 3.02227i 0.745341 + 0.860169i −0.204326 + 2.82104i −4.49462 − 1.31974i −0.173169 − 0.0464564i
11.20 1.36931 − 0.353547i −0.119292 + 0.829693i 1.75001 − 0.968228i −1.57873 + 0.463558i 0.129988 + 1.17828i 1.68916 + 1.94939i 2.05399 − 1.94451i 2.20432 + 0.647247i −1.99788 + 1.19291i
See next 80 embeddings (of 220 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 11.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner
23.d odd 22 1 inner
184.j even 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 184.2.j.a ✓ 220
4.b odd 2 1 736.2.r.a 220
8.b even 2 1 736.2.r.a 220
8.d odd 2 1 inner 184.2.j.a ✓ 220
23.d odd 22 1 inner 184.2.j.a ✓ 220
92.h even 22 1 736.2.r.a 220
184.j even 22 1 inner 184.2.j.a ✓ 220
184.m odd 22 1 736.2.r.a 220
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
184.2.j.a ✓ 220 1.a even 1 1 trivial
184.2.j.a ✓ 220 8.d odd 2 1 inner
184.2.j.a ✓ 220 23.d odd 22 1 inner
184.2.j.a ✓ 220 184.j even 22 1 inner
736.2.r.a 220 4.b odd 2 1
736.2.r.a 220 8.b even 2 1
736.2.r.a 220 92.h even 22 1
736.2.r.a 220 184.m odd 22 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(184, [\chi])\).