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Properties

Label 931.2.c.f
Level $931$
Weight $2$
Character orbit 931.c
Analytic conductor $7.434$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [931,2,Mod(930,931)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(931, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("931.930");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.c (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: \(7.43407242818\)
Analytic rank: \(0\)
Dimension: \(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 40 q^{4} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q - 40 q^{4} + 40 q^{9} + 40 q^{16} + 48 q^{23} - 56 q^{25} - 64 q^{30} - 40 q^{36} + 32 q^{39} - 16 q^{43} - 48 q^{57} - 96 q^{58} + 56 q^{64} + 144 q^{74} - 88 q^{81} - 160 q^{85} - 48 q^{92} + 72 q^{95} - 48 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
930.1 − 2.63313i −2.79849 −4.93337 3.67831i 7.36878i 0 7.72393i 4.83154 9.68547
930.2 − 2.63313i 2.79849 −4.93337 − 3.67831i − 7.36878i 0 7.72393i 4.83154 −9.68547
930.3 − 2.46413i −1.27582 −4.07192 0.595252i 3.14379i 0 5.10547i −1.37227 1.46678
930.4 − 2.46413i 1.27582 −4.07192 − 0.595252i − 3.14379i 0 5.10547i −1.37227 −1.46678
930.5 − 2.27541i −2.74153 −3.17751 − 1.16914i 6.23811i 0 2.67932i 4.51598 −2.66029
930.6 − 2.27541i 2.74153 −3.17751 1.16914i − 6.23811i 0 2.67932i 4.51598 2.66029
930.7 − 2.17125i −0.445561 −2.71434 − 3.02134i 0.967426i 0 1.55101i −2.80148 −6.56009
930.8 − 2.17125i 0.445561 −2.71434 3.02134i − 0.967426i 0 1.55101i −2.80148 6.56009
930.9 − 1.82908i −0.702444 −1.34552 2.40246i 1.28482i 0 − 1.19710i −2.50657 4.39428
930.10 − 1.82908i 0.702444 −1.34552 − 2.40246i − 1.28482i 0 − 1.19710i −2.50657 −4.39428
930.11 − 1.38421i −2.17908 0.0839688 − 4.26946i 3.01629i 0 − 2.88465i 1.74837 −5.90982
930.12 − 1.38421i 2.17908 0.0839688 4.26946i − 3.01629i 0 − 2.88465i 1.74837 5.90982
930.13 − 0.894152i −1.05130 1.20049 0.287796i 0.940021i 0 − 2.86173i −1.89477 0.257333
930.14 − 0.894152i 1.05130 1.20049 − 0.287796i − 0.940021i 0 − 2.86173i −1.89477 −0.257333
930.15 − 0.777313i −1.65913 1.39578 0.862792i 1.28966i 0 − 2.63959i −0.247282 0.670659
930.16 − 0.777313i 1.65913 1.39578 − 0.862792i − 1.28966i 0 − 2.63959i −0.247282 −0.670659
930.17 − 0.631664i −2.43801 1.60100 2.68891i 1.54000i 0 − 2.27462i 2.94387 1.69849
930.18 − 0.631664i 2.43801 1.60100 − 2.68891i − 1.54000i 0 − 2.27462i 2.94387 −1.69849
930.19 − 0.196456i −2.78973 1.96140 2.75005i 0.548060i 0 − 0.778243i 4.78260 0.540264
930.20 − 0.196456i 2.78973 1.96140 − 2.75005i − 0.548060i 0 − 0.778243i 4.78260 −0.540264
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 930.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
19.b odd 2 1 inner
133.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 931.2.c.f ✓ 40
7.b odd 2 1 inner 931.2.c.f ✓ 40
7.c even 3 2 931.2.o.i 80
7.d odd 6 2 931.2.o.i 80
19.b odd 2 1 inner 931.2.c.f ✓ 40
133.c even 2 1 inner 931.2.c.f ✓ 40
133.o even 6 2 931.2.o.i 80
133.r odd 6 2 931.2.o.i 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
931.2.c.f ✓ 40 1.a even 1 1 trivial
931.2.c.f ✓ 40 7.b odd 2 1 inner
931.2.c.f ✓ 40 19.b odd 2 1 inner
931.2.c.f ✓ 40 133.c even 2 1 inner
931.2.o.i 80 7.c even 3 2
931.2.o.i 80 7.d odd 6 2
931.2.o.i 80 133.o even 6 2
931.2.o.i 80 133.r odd 6 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(931, [\chi])\):

\( T_{2}^{20} + 30 T_{2}^{18} + 375 T_{2}^{16} + 2532 T_{2}^{14} + 10017 T_{2}^{12} + 23614 T_{2}^{10} + \cdots + 49 \) Copy content Toggle raw display
\( T_{3}^{20} - 40 T_{3}^{18} + 676 T_{3}^{16} - 6280 T_{3}^{14} + 34977 T_{3}^{12} - 119720 T_{3}^{10} + \cdots + 6272 \) Copy content Toggle raw display