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Properties

Label 855.2.i.c
Level $855$
Weight $2$
Character orbit 855.i
Analytic conductor $6.827$
Analytic rank $0$
Dimension $42$
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] = [855,2,Mod(286,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.286");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.i (of order \(3\), degree \(2\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 42 q - 3 q^{2} - 2 q^{3} - 23 q^{4} - 21 q^{5} - q^{6} - 2 q^{7} + 24 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 42 q - 3 q^{2} - 2 q^{3} - 23 q^{4} - 21 q^{5} - q^{6} - 2 q^{7} + 24 q^{8} + 6 q^{9} + 6 q^{10} - q^{11} - 11 q^{12} - 13 q^{13} - 9 q^{14} + q^{15} - 23 q^{16} + 14 q^{17} + 42 q^{18} - 42 q^{19} - 23 q^{20} + 2 q^{21} - 19 q^{22} - 7 q^{23} - 32 q^{24} - 21 q^{25} - 12 q^{26} - 11 q^{27} + 16 q^{28} - 4 q^{29} - 4 q^{30} - 16 q^{31} - 17 q^{32} - 33 q^{33} - 18 q^{34} + 4 q^{35} - 25 q^{36} + 22 q^{37} + 3 q^{38} + 4 q^{39} - 12 q^{40} - 4 q^{41} + 17 q^{42} + 6 q^{43} + 80 q^{44} - 9 q^{45} + 72 q^{46} - 8 q^{47} + 47 q^{48} - 53 q^{49} - 3 q^{50} + 44 q^{51} - 58 q^{52} + 50 q^{53} + 23 q^{54} + 2 q^{55} - 14 q^{56} + 2 q^{57} - 31 q^{58} + 3 q^{59} + 19 q^{60} - 38 q^{61} - 26 q^{62} - 27 q^{63} + 72 q^{64} - 13 q^{65} + 34 q^{66} - 16 q^{67} - 38 q^{68} - 59 q^{69} - 9 q^{70} + 22 q^{71} - 50 q^{72} + 94 q^{73} + 13 q^{74} + q^{75} + 23 q^{76} - 32 q^{77} - 93 q^{78} - 35 q^{79} + 46 q^{80} - 14 q^{81} + 96 q^{82} - 26 q^{83} + 71 q^{84} - 7 q^{85} + 55 q^{86} + 46 q^{87} - 50 q^{88} + 8 q^{89} - 18 q^{90} + 8 q^{91} - 2 q^{92} + 52 q^{93} - 32 q^{94} + 21 q^{95} + 2 q^{96} - 66 q^{97} + 144 q^{98} - 45 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
286.1 −1.36014 + 2.35582i 0.703446 − 1.58277i −2.69994 − 4.67643i −0.500000 − 0.866025i 2.77195 + 3.80998i −0.840910 + 1.45650i 9.24858 −2.01033 − 2.22679i 2.72027
286.2 −1.32853 + 2.30108i −1.60365 + 0.654449i −2.52999 − 4.38207i −0.500000 − 0.866025i 0.624559 − 4.55959i 2.20553 − 3.82008i 8.13054 2.14339 − 2.09901i 2.65706
286.3 −1.25449 + 2.17285i −0.405158 + 1.68400i −2.14751 − 3.71959i −0.500000 − 0.866025i −3.15080 − 2.99291i −2.28384 + 3.95573i 5.75817 −2.67169 − 1.36457i 2.50899
286.4 −1.11107 + 1.92443i −1.62389 − 0.602485i −1.46896 − 2.54431i −0.500000 − 0.866025i 2.96369 − 2.45566i −1.45222 + 2.51533i 2.08417 2.27402 + 1.95674i 2.22214
286.5 −0.882434 + 1.52842i 1.42056 − 0.990968i −0.557379 − 0.965408i −0.500000 − 0.866025i 0.261067 + 3.04567i −1.58136 + 2.73900i −1.56234 1.03597 − 2.81545i 1.76487
286.6 −0.851308 + 1.47451i 1.64629 + 0.538264i −0.449452 − 0.778473i −0.500000 − 0.866025i −2.19518 + 1.96924i 0.346026 − 0.599335i −1.87475 2.42054 + 1.77228i 1.70262
286.7 −0.805815 + 1.39571i 0.304546 + 1.70507i −0.298675 − 0.517319i −0.500000 − 0.866025i −2.62519 − 0.948909i 2.08396 − 3.60953i −2.26055 −2.81450 + 1.03854i 1.61163
286.8 −0.599096 + 1.03767i 1.07933 − 1.35464i 0.282167 + 0.488728i −0.500000 − 0.866025i 0.759044 + 1.93154i 2.21377 − 3.83437i −3.07257 −0.670107 − 2.92420i 1.19819
286.9 −0.474192 + 0.821324i −0.694928 − 1.58653i 0.550285 + 0.953121i −0.500000 − 0.866025i 1.63258 + 0.181558i 0.101824 − 0.176364i −2.94053 −2.03415 + 2.20505i 0.948383
286.10 −0.316751 + 0.548629i −1.70134 + 0.324708i 0.799338 + 1.38449i −0.500000 − 0.866025i 0.360758 − 1.03626i −2.17684 + 3.77040i −2.27977 2.78913 − 1.10488i 0.633502
286.11 0.0971337 − 0.168240i −1.23627 + 1.21311i 0.981130 + 1.69937i −0.500000 − 0.866025i 0.0840115 + 0.325824i 0.318566 − 0.551773i 0.769738 0.0567138 − 2.99946i −0.194267
286.12 0.172475 − 0.298736i 1.26618 + 1.18186i 0.940504 + 1.62900i −0.500000 − 0.866025i 0.571448 − 0.174414i −2.32282 + 4.02325i 1.33876 0.206436 + 2.99289i −0.344951
286.13 0.225215 − 0.390085i −1.27674 − 1.17045i 0.898556 + 1.55634i −0.500000 − 0.866025i −0.744114 + 0.234433i −0.111525 + 0.193167i 1.71034 0.260117 + 2.98870i −0.450431
286.14 0.383983 − 0.665078i −0.0349917 + 1.73170i 0.705114 + 1.22129i −0.500000 − 0.866025i 1.13828 + 0.688214i 0.997184 − 1.72717i 2.61894 −2.99755 − 0.121190i −0.767966
286.15 0.464365 − 0.804304i 1.38545 − 1.03949i 0.568730 + 0.985070i −0.500000 − 0.866025i −0.192711 − 1.59702i 1.54520 − 2.67637i 2.91385 0.838929 − 2.88031i −0.928730
286.16 0.780479 − 1.35183i 0.362372 + 1.69372i −0.218294 − 0.378096i −0.500000 − 0.866025i 2.57244 + 0.832047i −0.395362 + 0.684787i 2.44042 −2.73737 + 1.22751i −1.56096
286.17 0.819025 − 1.41859i 1.55409 − 0.764719i −0.341603 − 0.591673i −0.500000 − 0.866025i 0.188017 − 2.83095i −1.50427 + 2.60546i 2.15697 1.83041 − 2.37689i −1.63805
286.18 0.886025 − 1.53464i −1.64126 + 0.553424i −0.570080 − 0.987408i −0.500000 − 0.866025i −0.604888 + 3.00909i 1.04850 − 1.81606i 1.52368 2.38744 − 1.81662i −1.77205
286.19 1.10809 − 1.91926i −1.55693 − 0.758924i −1.45572 − 2.52137i −0.500000 − 0.866025i −3.18179 + 2.14721i 2.04715 − 3.54576i −2.01989 1.84807 + 2.36318i −2.21618
286.20 1.25907 − 2.18078i −0.671047 − 1.59678i −2.17053 − 3.75947i −0.500000 − 0.866025i −4.32711 − 0.547053i −1.86883 + 3.23690i −5.89513 −2.09939 + 2.14303i −2.51815
See all 42 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 286.21
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
9.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 855.2.i.c ✓ 42
9.c even 3 1 inner 855.2.i.c ✓ 42
9.c even 3 1 7695.2.a.v 21
9.d odd 6 1 7695.2.a.u 21
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
855.2.i.c ✓ 42 1.a even 1 1 trivial
855.2.i.c ✓ 42 9.c even 3 1 inner
7695.2.a.u 21 9.d odd 6 1
7695.2.a.v 21 9.c even 3 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{42} + 3 T_{2}^{41} + 37 T_{2}^{40} + 86 T_{2}^{39} + 712 T_{2}^{38} + 1422 T_{2}^{37} + \cdots + 38809 \) acting on \(S_{2}^{\mathrm{new}}(855, [\chi])\). Copy content Toggle raw display