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Properties

Label 183.2.h.b
Level $183$
Weight $2$
Character orbit 183.h
Analytic conductor $1.461$
Analytic rank $0$
Dimension $28$
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] = [183,2,Mod(34,183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(183, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("183.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 183 = 3 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 183.h (of order \(5\), degree \(4\), 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: \(1.46126235699\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 3 q^{2} - 7 q^{3} - 17 q^{4} + 2 q^{5} + 2 q^{6} + 10 q^{7} + q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - 3 q^{2} - 7 q^{3} - 17 q^{4} + 2 q^{5} + 2 q^{6} + 10 q^{7} + q^{8} - 7 q^{9} - 2 q^{10} - 4 q^{11} - 17 q^{12} + 10 q^{13} + 4 q^{14} + 2 q^{15} - 11 q^{16} - 8 q^{17} + 2 q^{18} - 18 q^{19} - 11 q^{20} - 6 q^{22} + 16 q^{23} - 4 q^{24} - q^{25} - q^{26} - 7 q^{27} + 36 q^{28} - 20 q^{29} - 2 q^{30} - 2 q^{31} + 44 q^{32} + q^{33} - 15 q^{34} + 6 q^{35} - 2 q^{36} - 14 q^{37} - q^{38} + 5 q^{39} + 4 q^{40} - 22 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} - 3 q^{45} - 5 q^{46} + 26 q^{47} + 74 q^{48} + 11 q^{49} - 26 q^{50} - 8 q^{51} - 16 q^{52} - 7 q^{53} - 3 q^{54} + 18 q^{55} + 11 q^{56} + 17 q^{57} - 11 q^{58} - 4 q^{59} - 16 q^{60} + 10 q^{61} + 158 q^{62} + 10 q^{63} - 37 q^{64} - 57 q^{65} - 6 q^{66} - 6 q^{67} + 118 q^{68} + 16 q^{69} - 81 q^{70} + 11 q^{71} + 6 q^{72} - 49 q^{73} - 54 q^{74} + 34 q^{75} + 25 q^{76} - 7 q^{77} - 21 q^{78} + 29 q^{79} - 81 q^{80} - 7 q^{81} - 30 q^{82} - 12 q^{83} - 29 q^{84} - 25 q^{85} - 54 q^{86} + 5 q^{87} - 62 q^{88} + 119 q^{89} + 8 q^{90} - 38 q^{91} - 132 q^{92} - 22 q^{93} - 10 q^{94} + 6 q^{95} - 16 q^{96} + 6 q^{97} - 71 q^{98} + q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
34.1 −2.22068 + 1.61342i −0.809017 + 0.587785i 1.71026 − 5.26365i 0.147735 − 0.454681i 0.848224 − 2.61056i 1.12717 + 0.818934i 2.99807 + 9.22712i 0.309017 − 0.951057i 0.405519 + 1.24806i
34.2 −1.22333 + 0.888804i −0.809017 + 0.587785i 0.0885390 − 0.272495i −0.638807 + 1.96605i 0.467272 − 1.43812i 3.17954 + 2.31007i −0.800662 − 2.46418i 0.309017 − 0.951057i −0.965956 − 2.97291i
34.3 −1.13825 + 0.826988i −0.809017 + 0.587785i −0.00632766 + 0.0194745i 1.04875 − 3.22773i 0.434773 − 1.33809i −2.17127 − 1.57752i −0.878449 − 2.70359i 0.309017 − 0.951057i 1.47555 + 4.54127i
34.4 −0.290294 + 0.210911i −0.809017 + 0.587785i −0.578247 + 1.77966i −0.484812 + 1.49210i 0.110882 − 0.341261i −3.58759 − 2.60654i −0.429253 − 1.32110i 0.309017 − 0.951057i −0.173962 − 0.535399i
34.5 0.573748 − 0.416853i −0.809017 + 0.587785i −0.462613 + 1.42378i 1.15372 − 3.55077i −0.219152 + 0.674482i 3.58479 + 2.60450i 0.766386 + 2.35869i 0.309017 − 0.951057i −0.818206 − 2.51818i
34.6 0.956750 − 0.695120i −0.809017 + 0.587785i −0.185855 + 0.572001i −0.849987 + 2.61599i −0.365446 + 1.12473i 0.0731827 + 0.0531703i 0.950685 + 2.92591i 0.309017 − 0.951057i 1.00520 + 3.09369i
34.7 2.03304 − 1.47709i −0.809017 + 0.587785i 1.33343 − 4.10386i 0.123404 − 0.379797i −0.776553 + 2.38998i 1.41220 + 1.02603i −1.79776 − 5.53295i 0.309017 − 0.951057i −0.310110 − 0.954421i
58.1 −0.827936 + 2.54813i 0.309017 − 0.951057i −4.18943 − 3.04380i 2.68685 + 1.95211i 2.16756 + 1.57483i 1.15806 + 3.56414i 6.88944 − 5.00547i −0.809017 − 0.587785i −7.19877 + 5.23021i
58.2 −0.694027 + 2.13600i 0.309017 − 0.951057i −2.46277 − 1.78931i −2.32511 − 1.68929i 1.81699 + 1.32012i −1.22347 − 3.76545i 1.89721 − 1.37841i −0.809017 − 0.587785i 5.22201 − 3.79401i
58.3 −0.376895 + 1.15996i 0.309017 − 0.951057i 0.414568 + 0.301202i −1.02522 − 0.744864i 0.986724 + 0.716897i 1.17397 + 3.61311i −2.47908 + 1.80116i −0.809017 − 0.587785i 1.25041 − 0.908480i
58.4 −0.136469 + 0.420008i 0.309017 − 0.951057i 1.46025 + 1.06093i 1.79319 + 1.30283i 0.357280 + 0.259579i −0.391244 − 1.20413i −1.35944 + 0.987691i −0.809017 − 0.587785i −0.791915 + 0.575360i
58.5 0.432088 − 1.32983i 0.309017 − 0.951057i 0.0362831 + 0.0263612i 1.21419 + 0.882159i −1.13122 − 0.821881i 0.0372257 + 0.114569i 2.31318 − 1.68062i −0.809017 − 0.587785i 1.69776 − 1.23349i
58.6 0.543987 − 1.67422i 0.309017 − 0.951057i −0.889056 − 0.645937i −3.22415 − 2.34248i −1.42418 − 1.03472i 0.555508 + 1.70968i 1.28328 − 0.932356i −0.809017 − 0.587785i −5.67573 + 4.12366i
58.7 0.868269 − 2.67226i 0.309017 − 0.951057i −4.76903 − 3.46490i 1.38025 + 1.00281i −2.27316 − 1.65155i 0.0719157 + 0.221334i −8.85360 + 6.43252i −0.809017 − 0.587785i 3.87819 − 2.81767i
70.1 −2.22068 − 1.61342i −0.809017 − 0.587785i 1.71026 + 5.26365i 0.147735 + 0.454681i 0.848224 + 2.61056i 1.12717 − 0.818934i 2.99807 − 9.22712i 0.309017 + 0.951057i 0.405519 − 1.24806i
70.2 −1.22333 − 0.888804i −0.809017 − 0.587785i 0.0885390 + 0.272495i −0.638807 − 1.96605i 0.467272 + 1.43812i 3.17954 − 2.31007i −0.800662 + 2.46418i 0.309017 + 0.951057i −0.965956 + 2.97291i
70.3 −1.13825 − 0.826988i −0.809017 − 0.587785i −0.00632766 − 0.0194745i 1.04875 + 3.22773i 0.434773 + 1.33809i −2.17127 + 1.57752i −0.878449 + 2.70359i 0.309017 + 0.951057i 1.47555 − 4.54127i
70.4 −0.290294 − 0.210911i −0.809017 − 0.587785i −0.578247 − 1.77966i −0.484812 − 1.49210i 0.110882 + 0.341261i −3.58759 + 2.60654i −0.429253 + 1.32110i 0.309017 + 0.951057i −0.173962 + 0.535399i
70.5 0.573748 + 0.416853i −0.809017 − 0.587785i −0.462613 − 1.42378i 1.15372 + 3.55077i −0.219152 − 0.674482i 3.58479 − 2.60450i 0.766386 − 2.35869i 0.309017 + 0.951057i −0.818206 + 2.51818i
70.6 0.956750 + 0.695120i −0.809017 − 0.587785i −0.185855 − 0.572001i −0.849987 − 2.61599i −0.365446 − 1.12473i 0.0731827 − 0.0531703i 0.950685 − 2.92591i 0.309017 + 0.951057i 1.00520 − 3.09369i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 34.7
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
61.e even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 183.2.h.b ✓ 28
3.b odd 2 1 549.2.k.c 28
61.e even 5 1 inner 183.2.h.b ✓ 28
183.n odd 10 1 549.2.k.c 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
183.2.h.b ✓ 28 1.a even 1 1 trivial
183.2.h.b ✓ 28 61.e even 5 1 inner
549.2.k.c 28 3.b odd 2 1
549.2.k.c 28 183.n odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{28} + 3 T_{2}^{27} + 20 T_{2}^{26} + 48 T_{2}^{25} + 204 T_{2}^{24} + 405 T_{2}^{23} + \cdots + 9801 \) acting on \(S_{2}^{\mathrm{new}}(183, [\chi])\). Copy content Toggle raw display