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Properties

Label 6930.2.f.a
Level $6930$
Weight $2$
Character orbit 6930.f
Analytic conductor $55.336$
Analytic rank $0$
Dimension $24$
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] = [6930,2,Mod(881,6930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6930, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6930.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6930.f (of order \(2\), degree \(1\), 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: \(55.3363286007\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{4} - 24 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{4} - 24 q^{5} + 24 q^{16} + 24 q^{20} - 24 q^{22} + 24 q^{25} + 16 q^{37} + 8 q^{38} + 32 q^{43} - 24 q^{47} - 24 q^{49} - 8 q^{58} - 8 q^{62} - 24 q^{64} - 32 q^{67} - 80 q^{79} - 24 q^{80} - 16 q^{83} + 24 q^{88} - 56 q^{89} + 24 q^{91} + 16 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
881.1 − 1.00000i 0 −1.00000 −1.00000 0 −2.55849 − 0.673900i 1.00000i 0 1.00000i
881.2 − 1.00000i 0 −1.00000 −1.00000 0 −2.53399 + 0.760838i 1.00000i 0 1.00000i
881.3 − 1.00000i 0 −1.00000 −1.00000 0 −1.32658 + 2.28915i 1.00000i 0 1.00000i
881.4 − 1.00000i 0 −1.00000 −1.00000 0 −1.10806 + 2.40254i 1.00000i 0 1.00000i
881.5 − 1.00000i 0 −1.00000 −1.00000 0 −0.749784 − 2.53729i 1.00000i 0 1.00000i
881.6 − 1.00000i 0 −1.00000 −1.00000 0 −0.575856 − 2.58232i 1.00000i 0 1.00000i
881.7 − 1.00000i 0 −1.00000 −1.00000 0 −0.263212 − 2.63263i 1.00000i 0 1.00000i
881.8 − 1.00000i 0 −1.00000 −1.00000 0 0.870461 + 2.49846i 1.00000i 0 1.00000i
881.9 − 1.00000i 0 −1.00000 −1.00000 0 1.13176 − 2.39147i 1.00000i 0 1.00000i
881.10 − 1.00000i 0 −1.00000 −1.00000 0 2.05578 + 1.66547i 1.00000i 0 1.00000i
881.11 − 1.00000i 0 −1.00000 −1.00000 0 2.41496 + 1.08072i 1.00000i 0 1.00000i
881.12 − 1.00000i 0 −1.00000 −1.00000 0 2.64301 + 0.120435i 1.00000i 0 1.00000i
881.13 1.00000i 0 −1.00000 −1.00000 0 −2.55849 + 0.673900i − 1.00000i 0 − 1.00000i
881.14 1.00000i 0 −1.00000 −1.00000 0 −2.53399 − 0.760838i − 1.00000i 0 − 1.00000i
881.15 1.00000i 0 −1.00000 −1.00000 0 −1.32658 − 2.28915i − 1.00000i 0 − 1.00000i
881.16 1.00000i 0 −1.00000 −1.00000 0 −1.10806 − 2.40254i − 1.00000i 0 − 1.00000i
881.17 1.00000i 0 −1.00000 −1.00000 0 −0.749784 + 2.53729i − 1.00000i 0 − 1.00000i
881.18 1.00000i 0 −1.00000 −1.00000 0 −0.575856 + 2.58232i − 1.00000i 0 − 1.00000i
881.19 1.00000i 0 −1.00000 −1.00000 0 −0.263212 + 2.63263i − 1.00000i 0 − 1.00000i
881.20 1.00000i 0 −1.00000 −1.00000 0 0.870461 − 2.49846i − 1.00000i 0 − 1.00000i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 881.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
21.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6930.2.f.a ✓ 24
3.b odd 2 1 6930.2.f.c yes 24
7.b odd 2 1 6930.2.f.c yes 24
21.c even 2 1 inner 6930.2.f.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6930.2.f.a ✓ 24 1.a even 1 1 trivial
6930.2.f.a ✓ 24 21.c even 2 1 inner
6930.2.f.c yes 24 3.b odd 2 1
6930.2.f.c yes 24 7.b odd 2 1