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Properties

Label 960.3.n.a
Level $960$
Weight $3$
Character orbit 960.n
Analytic conductor $26.158$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [960,3,Mod(161,960)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(960, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("960.161");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 960.n (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: \(26.1581053786\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 8 q^{9} + 120 q^{25} - 256 q^{33} + 104 q^{49} - 304 q^{57} + 400 q^{73} + 152 q^{81} + 208 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
161.1 0 −2.99223 − 0.215720i 0 −2.23607 0 −8.57552 0 8.90693 + 1.29097i 0
161.2 0 −2.99223 − 0.215720i 0 2.23607 0 8.57552 0 8.90693 + 1.29097i 0
161.3 0 −2.99223 + 0.215720i 0 −2.23607 0 −8.57552 0 8.90693 − 1.29097i 0
161.4 0 −2.99223 + 0.215720i 0 2.23607 0 8.57552 0 8.90693 − 1.29097i 0
161.5 0 −1.61015 − 2.53129i 0 −2.23607 0 8.16215 0 −3.81483 + 8.15151i 0
161.6 0 −1.61015 − 2.53129i 0 2.23607 0 −8.16215 0 −3.81483 + 8.15151i 0
161.7 0 −1.61015 + 2.53129i 0 −2.23607 0 8.16215 0 −3.81483 − 8.15151i 0
161.8 0 −1.61015 + 2.53129i 0 2.23607 0 −8.16215 0 −3.81483 − 8.15151i 0
161.9 0 −1.20580 − 2.74701i 0 −2.23607 0 −4.45418 0 −6.09210 + 6.62468i 0
161.10 0 −1.20580 − 2.74701i 0 2.23607 0 4.45418 0 −6.09210 + 6.62468i 0
161.11 0 −1.20580 + 2.74701i 0 −2.23607 0 −4.45418 0 −6.09210 − 6.62468i 0
161.12 0 −1.20580 + 2.74701i 0 2.23607 0 4.45418 0 −6.09210 − 6.62468i 0
161.13 0 1.20580 − 2.74701i 0 −2.23607 0 4.45418 0 −6.09210 − 6.62468i 0
161.14 0 1.20580 − 2.74701i 0 2.23607 0 −4.45418 0 −6.09210 − 6.62468i 0
161.15 0 1.20580 + 2.74701i 0 −2.23607 0 4.45418 0 −6.09210 + 6.62468i 0
161.16 0 1.20580 + 2.74701i 0 2.23607 0 −4.45418 0 −6.09210 + 6.62468i 0
161.17 0 1.61015 − 2.53129i 0 −2.23607 0 −8.16215 0 −3.81483 − 8.15151i 0
161.18 0 1.61015 − 2.53129i 0 2.23607 0 8.16215 0 −3.81483 − 8.15151i 0
161.19 0 1.61015 + 2.53129i 0 −2.23607 0 −8.16215 0 −3.81483 + 8.15151i 0
161.20 0 1.61015 + 2.53129i 0 2.23607 0 8.16215 0 −3.81483 + 8.15151i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 161.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
4.b odd 2 1 inner
8.b even 2 1 inner
8.d odd 2 1 inner
12.b even 2 1 inner
24.f even 2 1 inner
24.h odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 960.3.n.a ✓ 24
3.b odd 2 1 inner 960.3.n.a ✓ 24
4.b odd 2 1 inner 960.3.n.a ✓ 24
8.b even 2 1 inner 960.3.n.a ✓ 24
8.d odd 2 1 inner 960.3.n.a ✓ 24
12.b even 2 1 inner 960.3.n.a ✓ 24
24.f even 2 1 inner 960.3.n.a ✓ 24
24.h odd 2 1 inner 960.3.n.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
960.3.n.a ✓ 24 1.a even 1 1 trivial
960.3.n.a ✓ 24 3.b odd 2 1 inner
960.3.n.a ✓ 24 4.b odd 2 1 inner
960.3.n.a ✓ 24 8.b even 2 1 inner
960.3.n.a ✓ 24 8.d odd 2 1 inner
960.3.n.a ✓ 24 12.b even 2 1 inner
960.3.n.a ✓ 24 24.f even 2 1 inner
960.3.n.a ✓ 24 24.h odd 2 1 inner