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Properties

Label 201.3.l.a
Level $201$
Weight $3$
Character orbit 201.l
Analytic conductor $5.477$
Analytic rank $0$
Dimension $220$
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] = [201,3,Mod(43,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.43");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.l (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: \(5.47685331364\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9} - 162 q^{10} - 72 q^{14} + 54 q^{15} - 116 q^{16} + 14 q^{17} - 84 q^{19} - 48 q^{21} + 78 q^{22} + 82 q^{23} - 36 q^{24} + 62 q^{25} + 100 q^{26} - 154 q^{28} + 52 q^{29} - 88 q^{31} + 770 q^{32} - 36 q^{33} + 180 q^{35} + 42 q^{36} - 304 q^{37} + 72 q^{39} - 1066 q^{40} + 330 q^{41} + 770 q^{43} - 242 q^{46} - 616 q^{47} - 146 q^{49} + 858 q^{50} + 264 q^{52} - 286 q^{53} - 62 q^{55} - 1484 q^{56} - 660 q^{57} - 352 q^{58} - 634 q^{59} - 504 q^{60} - 352 q^{61} + 124 q^{62} - 132 q^{63} - 1226 q^{64} + 196 q^{65} + 156 q^{67} - 192 q^{68} + 66 q^{69} + 1144 q^{70} + 280 q^{71} + 264 q^{72} + 552 q^{73} + 352 q^{74} + 396 q^{75} + 400 q^{76} - 176 q^{77} + 528 q^{78} + 682 q^{79} + 1848 q^{80} - 198 q^{81} + 728 q^{82} + 246 q^{83} - 1320 q^{84} - 1120 q^{86} + 1120 q^{88} + 448 q^{89} + 486 q^{90} - 128 q^{91} + 604 q^{92} + 72 q^{93} + 704 q^{94} - 462 q^{95} + 144 q^{96} - 176 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
43.1 −3.38399 − 1.54542i 0.936417 + 1.45709i 6.44363 + 7.43634i 1.51116 + 0.217272i −0.917010 − 6.37794i 8.17740 + 3.73449i −6.12054 − 20.8446i −1.24625 + 2.72890i −4.77798 − 3.07062i
43.2 −3.31598 − 1.51436i −0.936417 − 1.45709i 6.08302 + 7.02018i −3.45931 − 0.497373i 0.898581 + 6.24977i 4.95524 + 2.26298i −5.43199 − 18.4997i −1.24625 + 2.72890i 10.7178 + 6.88791i
43.3 −2.57988 − 1.17819i −0.936417 − 1.45709i 2.64821 + 3.05620i 4.45790 + 0.640949i 0.699109 + 4.86241i −4.40917 − 2.01360i −0.0350994 − 0.119537i −1.24625 + 2.72890i −10.7457 − 6.90583i
43.4 −2.54688 − 1.16312i 0.936417 + 1.45709i 2.51429 + 2.90164i 1.62480 + 0.233611i −0.690165 − 4.80020i −7.97050 − 3.64000i 0.126668 + 0.431390i −1.24625 + 2.72890i −3.86645 − 2.48482i
43.5 −2.27098 − 1.03712i −0.936417 − 1.45709i 1.46229 + 1.68758i 2.84282 + 0.408736i 0.615402 + 4.28021i −0.295181 − 0.134805i 1.24287 + 4.23283i −1.24625 + 2.72890i −6.03208 − 3.87658i
43.6 −1.91347 − 0.873852i 0.936417 + 1.45709i 0.278305 + 0.321181i 9.57220 + 1.37628i −0.518521 − 3.60640i 5.09555 + 2.32706i 2.11871 + 7.21565i −1.24625 + 2.72890i −17.1135 − 10.9982i
43.7 −1.73436 − 0.792054i −0.936417 − 1.45709i −0.238801 − 0.275591i −8.70735 − 1.25193i 0.469984 + 3.26881i −9.89366 − 4.51828i 2.34455 + 7.98481i −1.24625 + 2.72890i 14.1101 + 9.06798i
43.8 −1.59211 − 0.727091i 0.936417 + 1.45709i −0.613300 − 0.707786i −8.19855 − 1.17877i −0.431437 − 3.00071i 10.0493 + 4.58935i 2.43425 + 8.29030i −1.24625 + 2.72890i 12.1959 + 7.83782i
43.9 −1.00045 − 0.456891i 0.936417 + 1.45709i −1.82729 − 2.10880i −2.48696 − 0.357570i −0.271107 − 1.88559i −2.35904 − 1.07734i 2.10407 + 7.16579i −1.24625 + 2.72890i 2.32471 + 1.49400i
43.10 −0.736337 − 0.336274i −0.936417 − 1.45709i −2.19033 − 2.52778i 5.35256 + 0.769582i 0.199536 + 1.38780i 8.86602 + 4.04898i 1.67503 + 5.70464i −1.24625 + 2.72890i −3.68250 − 2.36660i
43.11 −0.480619 − 0.219491i 0.936417 + 1.45709i −2.43662 − 2.81201i −0.667348 − 0.0959501i −0.130240 − 0.905842i −2.12406 − 0.970026i 1.14931 + 3.91418i −1.24625 + 2.72890i 0.299680 + 0.192592i
43.12 −0.139433 − 0.0636767i −0.936417 − 1.45709i −2.60406 − 3.00524i −4.85688 − 0.698314i 0.0377841 + 0.262794i 4.72724 + 2.15886i 0.344467 + 1.17315i −1.24625 + 2.72890i 0.632741 + 0.406638i
43.13 −0.132389 − 0.0604598i −0.936417 − 1.45709i −2.60557 − 3.00699i 5.16768 + 0.743001i 0.0358753 + 0.249518i −10.9487 − 5.00010i 0.327160 + 1.11420i −1.24625 + 2.72890i −0.639220 − 0.410802i
43.14 0.191268 + 0.0873493i 0.936417 + 1.45709i −2.59049 − 2.98958i 8.50765 + 1.22322i 0.0518308 + 0.360491i −5.30827 − 2.42421i −0.471300 − 1.60510i −1.24625 + 2.72890i 1.52040 + 0.977100i
43.15 1.40253 + 0.640516i 0.936417 + 1.45709i −1.06260 − 1.22631i −7.67747 − 1.10385i 0.380065 + 2.64341i −5.69858 − 2.60245i −2.44245 − 8.31820i −1.24625 + 2.72890i −10.0609 − 6.46573i
43.16 1.43499 + 0.655336i 0.936417 + 1.45709i −0.989723 − 1.14220i −0.383091 − 0.0550801i 0.388860 + 2.70458i 12.2137 + 5.57779i −2.44950 − 8.34222i −1.24625 + 2.72890i −0.513634 − 0.330092i
43.17 1.62013 + 0.739889i −0.936417 − 1.45709i −0.542056 − 0.625565i 0.289414 + 0.0416115i −0.439031 − 3.05353i −6.47623 − 2.95760i −2.42251 − 8.25031i −1.24625 + 2.72890i 0.438101 + 0.281550i
43.18 2.16194 + 0.987325i −0.936417 − 1.45709i 1.07973 + 1.24607i −7.15134 − 1.02821i −0.585853 − 4.07470i −3.35568 − 1.53249i −1.57437 − 5.36180i −1.24625 + 2.72890i −14.4456 − 9.28362i
43.19 2.26882 + 1.03614i −0.936417 − 1.45709i 1.45454 + 1.67863i 6.52672 + 0.938401i −0.614817 − 4.27615i 2.05853 + 0.940098i −1.25001 − 4.25713i −1.24625 + 2.72890i 13.8357 + 8.89165i
43.20 2.70381 + 1.23479i 0.936417 + 1.45709i 3.16643 + 3.65425i 4.86060 + 0.698849i 0.732691 + 5.09598i −0.313460 − 0.143152i 0.699474 + 2.38219i −1.24625 + 2.72890i 12.2792 + 7.89136i
See next 80 embeddings (of 220 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 43.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
67.f odd 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 201.3.l.a ✓ 220
67.f odd 22 1 inner 201.3.l.a ✓ 220
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
201.3.l.a ✓ 220 1.a even 1 1 trivial
201.3.l.a ✓ 220 67.f odd 22 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(201, [\chi])\).