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Properties

Label 184.3.m.a
Level $184$
Weight $3$
Character orbit 184.m
Analytic conductor $5.014$
Analytic rank $0$
Dimension $460$
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] = [184,3,Mod(5,184)]
 
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([0, 11, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("184.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 184.m (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: \(5.01363686423\)
Analytic rank: \(0\)
Dimension: \(460\)
Relative dimension: \(46\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 460 q - 7 q^{2} - 11 q^{4} - 26 q^{6} - 22 q^{7} - 28 q^{8} + 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 460 q - 7 q^{2} - 11 q^{4} - 26 q^{6} - 22 q^{7} - 28 q^{8} + 108 q^{9} - 11 q^{10} - 42 q^{12} - 11 q^{14} - 22 q^{15} - 27 q^{16} - 22 q^{17} - 28 q^{18} - 11 q^{20} + 12 q^{23} - 74 q^{24} - 208 q^{25} - 84 q^{26} - 11 q^{28} - 11 q^{30} + 110 q^{31} + 133 q^{32} - 22 q^{33} + 231 q^{34} - 501 q^{36} + 374 q^{38} + 42 q^{39} - 451 q^{40} - 18 q^{41} + 319 q^{42} - 88 q^{44} - 39 q^{46} - 40 q^{47} - 160 q^{48} + 220 q^{49} - 436 q^{50} + 714 q^{52} - 768 q^{54} + 82 q^{55} + 594 q^{56} - 22 q^{57} - 553 q^{58} + 319 q^{60} - 30 q^{62} - 22 q^{63} - 86 q^{64} - 22 q^{65} - 110 q^{66} - 250 q^{70} - 146 q^{71} + 533 q^{72} - 18 q^{73} - 198 q^{74} - 836 q^{76} - 704 q^{78} - 22 q^{79} - 1100 q^{80} - 292 q^{81} - 560 q^{82} - 1089 q^{84} - 561 q^{86} - 246 q^{87} - 275 q^{88} - 22 q^{89} - 264 q^{90} + 324 q^{92} - 331 q^{94} + 402 q^{95} + 909 q^{96} - 22 q^{97} + 413 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1 −1.99466 − 0.146108i −2.25437 − 1.95342i 3.95730 + 0.582871i −0.338480 + 2.35418i 4.21128 + 4.22578i 1.22221 − 0.558167i −7.80830 − 1.74082i −0.0145135 − 0.100943i 1.01912 − 4.64633i
5.2 −1.99356 + 0.160377i −2.99383 − 2.59417i 3.94856 − 0.639444i 1.22055 − 8.48912i 6.38442 + 4.69148i 6.70294 − 3.06113i −7.76913 + 1.90803i 0.952470 + 6.62457i −1.07178 + 17.1193i
5.3 −1.98840 + 0.215104i 4.36428 + 3.78167i 3.90746 − 0.855424i −0.150305 + 1.04539i −9.49138 − 6.58070i −8.17744 + 3.73451i −7.58559 + 2.54143i 3.46508 + 24.1002i 0.0739979 − 2.11099i
5.4 −1.94856 − 0.450661i 0.887391 + 0.768929i 3.59381 + 1.75628i 1.05932 − 7.36771i −1.38261 − 1.89822i −5.44630 + 2.48724i −6.21128 − 5.04182i −1.08462 − 7.54371i −5.38449 + 13.8791i
5.5 −1.92286 + 0.550093i 1.68686 + 1.46168i 3.39480 − 2.11550i −0.234526 + 1.63116i −4.04766 − 1.88267i 9.45161 − 4.31640i −5.36400 + 5.93527i −0.571821 − 3.97710i −0.446330 − 3.26552i
5.6 −1.88288 − 0.674354i −0.887391 − 0.768929i 3.09049 + 2.53946i −1.05932 + 7.36771i 1.15232 + 2.04622i −5.44630 + 2.48724i −4.10654 − 6.86559i −1.08462 − 7.54371i 6.96301 − 13.1582i
5.7 −1.75700 − 0.955478i 2.25437 + 1.95342i 2.17412 + 3.35756i 0.338480 − 2.35418i −2.09448 − 5.58616i 1.22221 − 0.558167i −0.611865 − 7.97657i −0.0145135 − 0.100943i −2.84408 + 3.81290i
5.8 −1.70543 + 1.04475i −1.80947 − 1.56791i 1.81700 − 3.56350i 0.00664893 − 0.0462444i 4.72401 + 0.783530i −11.5321 + 5.26651i 0.624193 + 7.97561i −0.465008 − 3.23420i 0.0369744 + 0.0858131i
5.9 −1.65282 + 1.12614i 0.715794 + 0.620239i 1.46360 − 3.72262i 0.577710 − 4.01806i −1.88156 − 0.219054i −1.58743 + 0.724953i 1.77314 + 7.80102i −1.15317 − 8.02047i 3.57006 + 7.29170i
5.10 −1.60723 + 1.19030i −3.31379 − 2.87142i 1.16637 − 3.82617i −1.06615 + 7.41521i 8.74387 + 0.670619i 5.19665 − 2.37323i 2.67966 + 7.53786i 1.45535 + 10.1222i −7.11278 − 13.1870i
5.11 −1.59038 − 1.21272i 2.99383 + 2.59417i 1.05863 + 3.85737i −1.22055 + 8.48912i −1.61534 − 7.75638i 6.70294 − 3.06113i 2.99427 − 7.41851i 0.952470 + 6.62457i 12.2360 − 12.0208i
5.12 −1.55645 − 1.25597i −4.36428 − 3.78167i 0.845097 + 3.90971i 0.150305 − 1.04539i 2.04315 + 11.3674i −8.17744 + 3.73451i 3.59511 − 7.14669i 3.46508 + 24.1002i −1.54692 + 1.43833i
5.13 −1.32021 − 1.50234i −1.68686 − 1.46168i −0.514081 + 3.96683i 0.234526 − 1.63116i 0.0310764 + 4.46397i 9.45161 − 4.31640i 6.63824 − 4.46473i −0.571821 − 3.97710i −2.76020 + 1.80114i
5.14 −1.19644 + 1.60266i 3.70785 + 3.21287i −1.13705 − 3.83499i 0.886986 − 6.16912i −9.58539 + 2.09842i 4.49987 − 2.05502i 7.50660 + 2.76603i 2.14479 + 14.9174i 8.82579 + 8.80253i
5.15 −1.12443 + 1.65398i 2.27975 + 1.97541i −1.47130 − 3.71958i −1.15687 + 8.04618i −5.83072 + 1.54944i −4.28195 + 1.95550i 7.80649 + 1.74891i 0.0141615 + 0.0984956i −12.0074 − 10.9608i
5.16 −0.869867 − 1.80093i 1.80947 + 1.56791i −2.48666 + 3.13313i −0.00664893 + 0.0462444i 1.24970 − 4.62260i −11.5321 + 5.26651i 7.80560 + 1.75289i −0.465008 − 3.23420i 0.0890663 − 0.0282522i
5.17 −0.840427 + 1.81485i −3.60238 − 3.12148i −2.58736 − 3.05050i 0.734266 − 5.10693i 8.69256 − 3.91441i −0.796366 + 0.363688i 7.71069 − 2.13196i 1.95267 + 13.5811i 8.65122 + 5.62459i
5.18 −0.781598 − 1.84095i −0.715794 − 0.620239i −2.77821 + 2.87777i −0.577710 + 4.01806i −0.582368 + 1.80252i −1.58743 + 0.724953i 7.46928 + 2.86529i −1.15317 − 8.02047i 7.84859 − 2.07697i
5.19 −0.708563 − 1.87028i 3.31379 + 2.87142i −2.99588 + 2.65042i 1.06615 − 7.41521i 3.02232 − 8.23229i 5.19665 − 2.37323i 7.07978 + 3.72514i 1.45535 + 10.1222i −14.6239 + 3.26015i
5.20 −0.645970 + 1.89281i −0.582919 − 0.505102i −3.16545 − 2.44539i −0.283918 + 1.97470i 1.33261 − 0.777073i 7.35777 − 3.36018i 6.67344 − 4.41193i −1.19617 − 8.31953i −3.55432 − 1.81300i
See next 80 embeddings (of 460 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5.46
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 184.3.m.a ✓ 460
8.b even 2 1 inner 184.3.m.a ✓ 460
23.d odd 22 1 inner 184.3.m.a ✓ 460
184.m odd 22 1 inner 184.3.m.a ✓ 460
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
184.3.m.a ✓ 460 1.a even 1 1 trivial
184.3.m.a ✓ 460 8.b even 2 1 inner
184.3.m.a ✓ 460 23.d odd 22 1 inner
184.3.m.a ✓ 460 184.m odd 22 1 inner

Hecke kernels

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