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Properties

Label 1596.2.cd.b
Level $1596$
Weight $2$
Character orbit 1596.cd
Analytic conductor $12.744$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1596,2,Mod(829,1596)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1596, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1596.829");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1596.cd (of order \(6\), degree \(2\), 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: \(12.7441241626\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{3} + 24 q^{9} - 6 q^{11} + 2 q^{13} + 16 q^{19} - 12 q^{23} + 18 q^{25} - 24 q^{27} + 3 q^{29} - 6 q^{31} + 6 q^{33} - 10 q^{35} - 27 q^{37} - 2 q^{39} + 2 q^{41} - 22 q^{49} + 30 q^{53} - 21 q^{55}+ \cdots - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
829.1 0 −1.00000 0 −3.62701 − 2.09405i 0 1.40494 − 2.24191i 0 1.00000 0
829.2 0 −1.00000 0 −3.04103 − 1.75574i 0 −1.25932 + 2.32683i 0 1.00000 0
829.3 0 −1.00000 0 −2.24922 − 1.29859i 0 1.31222 + 2.29740i 0 1.00000 0
829.4 0 −1.00000 0 −1.15596 − 0.667396i 0 −2.63196 − 0.269795i 0 1.00000 0
829.5 0 −1.00000 0 −1.07458 − 0.620410i 0 2.12294 − 1.57896i 0 1.00000 0
829.6 0 −1.00000 0 −0.507458 − 0.292981i 0 1.73296 + 1.99921i 0 1.00000 0
829.7 0 −1.00000 0 0.105013 + 0.0606296i 0 −2.22446 − 1.43240i 0 1.00000 0
829.8 0 −1.00000 0 1.64485 + 0.949653i 0 0.857533 − 2.50293i 0 1.00000 0
829.9 0 −1.00000 0 1.87734 + 1.08388i 0 −1.67127 + 2.05106i 0 1.00000 0
829.10 0 −1.00000 0 2.30666 + 1.33175i 0 2.46098 + 0.971390i 0 1.00000 0
829.11 0 −1.00000 0 2.43610 + 1.40648i 0 −0.923140 + 2.47948i 0 1.00000 0
829.12 0 −1.00000 0 3.28530 + 1.89677i 0 −1.18143 − 2.36732i 0 1.00000 0
901.1 0 −1.00000 0 −3.62701 + 2.09405i 0 1.40494 + 2.24191i 0 1.00000 0
901.2 0 −1.00000 0 −3.04103 + 1.75574i 0 −1.25932 − 2.32683i 0 1.00000 0
901.3 0 −1.00000 0 −2.24922 + 1.29859i 0 1.31222 − 2.29740i 0 1.00000 0
901.4 0 −1.00000 0 −1.15596 + 0.667396i 0 −2.63196 + 0.269795i 0 1.00000 0
901.5 0 −1.00000 0 −1.07458 + 0.620410i 0 2.12294 + 1.57896i 0 1.00000 0
901.6 0 −1.00000 0 −0.507458 + 0.292981i 0 1.73296 − 1.99921i 0 1.00000 0
901.7 0 −1.00000 0 0.105013 − 0.0606296i 0 −2.22446 + 1.43240i 0 1.00000 0
901.8 0 −1.00000 0 1.64485 − 0.949653i 0 0.857533 + 2.50293i 0 1.00000 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 829.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
133.s even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1596.2.cd.b yes 24
7.d odd 6 1 1596.2.u.b ✓ 24
19.d odd 6 1 1596.2.u.b ✓ 24
133.s even 6 1 inner 1596.2.cd.b yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1596.2.u.b ✓ 24 7.d odd 6 1
1596.2.u.b ✓ 24 19.d odd 6 1
1596.2.cd.b yes 24 1.a even 1 1 trivial
1596.2.cd.b yes 24 133.s even 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{24} - 39 T_{5}^{22} + 977 T_{5}^{20} - 270 T_{5}^{19} - 14473 T_{5}^{18} + 6564 T_{5}^{17} + \cdots + 276676 \) acting on \(S_{2}^{\mathrm{new}}(1596, [\chi])\). Copy content Toggle raw display