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Properties

Label 1792.3.g.h
Level $1792$
Weight $3$
Character orbit 1792.g
Analytic conductor $48.828$
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] = [1792,3,Mod(127,1792)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1792.127");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1792.g (of order \(2\), degree \(1\), not 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: \(48.8284633734\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 896)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 16 q^{3} + 72 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 16 q^{3} + 72 q^{9} - 48 q^{11} + 16 q^{17} - 48 q^{19} - 72 q^{25} - 64 q^{27} + 32 q^{33} + 16 q^{41} + 208 q^{43} - 168 q^{49} - 96 q^{51} - 160 q^{57} - 368 q^{59} - 160 q^{65} + 400 q^{67} - 144 q^{73} + 400 q^{75} - 8 q^{81} - 464 q^{83} + 240 q^{89} + 224 q^{91} + 144 q^{97} + 1136 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
127.1 0 −5.37458 0 − 1.51324i 0 − 2.64575i 0 19.8861 0
127.2 0 −5.37458 0 1.51324i 0 2.64575i 0 19.8861 0
127.3 0 −4.72906 0 − 5.71623i 0 2.64575i 0 13.3640 0
127.4 0 −4.72906 0 5.71623i 0 − 2.64575i 0 13.3640 0
127.5 0 −4.16987 0 − 3.41703i 0 2.64575i 0 8.38785 0
127.6 0 −4.16987 0 3.41703i 0 − 2.64575i 0 8.38785 0
127.7 0 −3.42243 0 − 9.08210i 0 − 2.64575i 0 2.71304 0
127.8 0 −3.42243 0 9.08210i 0 2.64575i 0 2.71304 0
127.9 0 −2.58165 0 7.56987i 0 − 2.64575i 0 −2.33507 0
127.10 0 −2.58165 0 − 7.56987i 0 2.64575i 0 −2.33507 0
127.11 0 −2.16526 0 − 0.268166i 0 − 2.64575i 0 −4.31166 0
127.12 0 −2.16526 0 0.268166i 0 2.64575i 0 −4.31166 0
127.13 0 0.0923806 0 − 6.77038i 0 − 2.64575i 0 −8.99147 0
127.14 0 0.0923806 0 6.77038i 0 2.64575i 0 −8.99147 0
127.15 0 1.17566 0 − 0.487772i 0 − 2.64575i 0 −7.61783 0
127.16 0 1.17566 0 0.487772i 0 2.64575i 0 −7.61783 0
127.17 0 1.72633 0 8.41485i 0 2.64575i 0 −6.01977 0
127.18 0 1.72633 0 − 8.41485i 0 − 2.64575i 0 −6.01977 0
127.19 0 2.71141 0 − 3.78141i 0 2.64575i 0 −1.64827 0
127.20 0 2.71141 0 3.78141i 0 − 2.64575i 0 −1.64827 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 127.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1792.3.g.h 24
4.b odd 2 1 1792.3.g.i 24
8.b even 2 1 1792.3.g.i 24
8.d odd 2 1 inner 1792.3.g.h 24
16.e even 4 1 896.3.d.a ✓ 24
16.e even 4 1 896.3.d.b yes 24
16.f odd 4 1 896.3.d.a ✓ 24
16.f odd 4 1 896.3.d.b yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
896.3.d.a ✓ 24 16.e even 4 1
896.3.d.a ✓ 24 16.f odd 4 1
896.3.d.b yes 24 16.e even 4 1
896.3.d.b yes 24 16.f odd 4 1
1792.3.g.h 24 1.a even 1 1 trivial
1792.3.g.h 24 8.d odd 2 1 inner
1792.3.g.i 24 4.b odd 2 1
1792.3.g.i 24 8.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} + 8 T_{3}^{11} - 40 T_{3}^{10} - 432 T_{3}^{9} + 200 T_{3}^{8} + 7360 T_{3}^{7} + \cdots + 18432 \) acting on \(S_{3}^{\mathrm{new}}(1792, [\chi])\). Copy content Toggle raw display