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Properties

Label 920.2.y.d
Level $920$
Weight $2$
Character orbit 920.y
Analytic conductor $7.346$
Analytic rank $0$
Dimension $70$
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] = [920,2,Mod(41,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.y (of order \(11\), 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: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(7\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 70 q + q^{3} - 7 q^{5} - 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 70 q + q^{3} - 7 q^{5} - 20 q^{7} - 5 q^{11} + 10 q^{13} + q^{15} - 18 q^{17} + 2 q^{19} - 3 q^{23} - 7 q^{25} - 23 q^{27} - 6 q^{29} + 17 q^{31} - 5 q^{33} + 13 q^{35} - 29 q^{37} + 7 q^{39} - q^{41} + 36 q^{43} + 110 q^{45} + 20 q^{47} - 15 q^{49} + 46 q^{51} - 42 q^{53} + 6 q^{55} - 10 q^{57} + 49 q^{59} + 35 q^{61} + 31 q^{63} - 23 q^{65} - 32 q^{67} + 38 q^{69} + 10 q^{71} - 2 q^{73} + q^{75} - 87 q^{77} - 47 q^{79} + 121 q^{81} - 43 q^{83} + 4 q^{85} - 191 q^{87} - 69 q^{89} + 98 q^{91} + 94 q^{93} + 24 q^{95} - 23 q^{97} - 225 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
41.1 0 −1.87001 + 2.15810i 0 −0.142315 + 0.989821i 0 1.77408 + 3.88469i 0 −0.733537 − 5.10186i 0
41.2 0 −1.65473 + 1.90966i 0 −0.142315 + 0.989821i 0 −1.76863 − 3.87276i 0 −0.481726 − 3.35048i 0
41.3 0 −1.52351 + 1.75822i 0 −0.142315 + 0.989821i 0 −0.352964 − 0.772883i 0 −0.343322 − 2.38786i 0
41.4 0 −0.254301 + 0.293478i 0 −0.142315 + 0.989821i 0 1.51491 + 3.31720i 0 0.405484 + 2.82020i 0
41.5 0 0.678559 − 0.783099i 0 −0.142315 + 0.989821i 0 −1.37770 − 3.01675i 0 0.274143 + 1.90671i 0
41.6 0 1.02202 − 1.17947i 0 −0.142315 + 0.989821i 0 0.159343 + 0.348913i 0 0.0803105 + 0.558572i 0
41.7 0 1.69043 − 1.95086i 0 −0.142315 + 0.989821i 0 −1.43649 − 3.14548i 0 −0.521362 − 3.62615i 0
81.1 0 −0.451672 + 3.14145i 0 −0.959493 + 0.281733i 0 −2.48316 − 2.86572i 0 −6.78622 − 1.99262i 0
81.2 0 −0.237077 + 1.64891i 0 −0.959493 + 0.281733i 0 0.991521 + 1.14428i 0 0.215784 + 0.0633598i 0
81.3 0 −0.229990 + 1.59961i 0 −0.959493 + 0.281733i 0 0.0267928 + 0.0309205i 0 0.372610 + 0.109408i 0
81.4 0 0.0345352 − 0.240198i 0 −0.959493 + 0.281733i 0 −1.67072 − 1.92811i 0 2.82198 + 0.828607i 0
81.5 0 0.228525 − 1.58942i 0 −0.959493 + 0.281733i 0 2.37221 + 2.73768i 0 0.404436 + 0.118753i 0
81.6 0 0.262987 − 1.82912i 0 −0.959493 + 0.281733i 0 −1.02468 − 1.18254i 0 −0.398032 − 0.116873i 0
81.7 0 0.489823 − 3.40679i 0 −0.959493 + 0.281733i 0 −1.02915 − 1.18770i 0 −8.48784 − 2.49226i 0
121.1 0 −3.29427 − 0.967284i 0 0.841254 − 0.540641i 0 0.587665 − 4.08730i 0 7.39279 + 4.75106i 0
121.2 0 −2.56117 − 0.752028i 0 0.841254 − 0.540641i 0 −0.727818 + 5.06209i 0 3.47029 + 2.23022i 0
121.3 0 −0.873071 − 0.256357i 0 0.841254 − 0.540641i 0 0.0943504 − 0.656221i 0 −1.82723 − 1.17429i 0
121.4 0 0.213266 + 0.0626205i 0 0.841254 − 0.540641i 0 −0.242736 + 1.68827i 0 −2.48220 − 1.59521i 0
121.5 0 1.00987 + 0.296524i 0 0.841254 − 0.540641i 0 0.261523 − 1.81893i 0 −1.59185 − 1.02302i 0
121.6 0 2.29131 + 0.672789i 0 0.841254 − 0.540641i 0 −0.477634 + 3.32202i 0 2.27369 + 1.46121i 0
See all 70 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 41.7
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 920.2.y.d ✓ 70
23.c even 11 1 inner 920.2.y.d ✓ 70
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
920.2.y.d ✓ 70 1.a even 1 1 trivial
920.2.y.d ✓ 70 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{70} - T_{3}^{69} + 11 T_{3}^{68} - 5 T_{3}^{67} + 56 T_{3}^{66} - 162 T_{3}^{65} + \cdots + 136103395664896 \) acting on \(S_{2}^{\mathrm{new}}(920, [\chi])\). Copy content Toggle raw display