Properties

Label 2736.2.cg.a
Level $2736$
Weight $2$
Character orbit 2736.cg
Analytic conductor $21.847$
Analytic rank $0$
Dimension $24$
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] = [2736,2,Mod(1151,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.1151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.cg (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: \(21.8470699930\)
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 dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 12 q^{13} - 12 q^{19} + 8 q^{25} + 16 q^{37} - 12 q^{43} + 16 q^{49} + 12 q^{55} - 60 q^{67} + 8 q^{73} + 12 q^{79} + 16 q^{85} - 12 q^{91} - 32 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1151.1 0 0 0 −3.43403 1.98264i 0 2.01359i 0 0 0
1151.2 0 0 0 −2.27729 1.31480i 0 3.01718i 0 0 0
1151.3 0 0 0 −2.15944 1.24676i 0 0.872468i 0 0 0
1151.4 0 0 0 −1.62081 0.935772i 0 2.07786i 0 0 0
1151.5 0 0 0 −1.02690 0.592883i 0 4.00663i 0 0 0
1151.6 0 0 0 −0.420258 0.242636i 0 1.92619i 0 0 0
1151.7 0 0 0 0.420258 + 0.242636i 0 1.92619i 0 0 0
1151.8 0 0 0 1.02690 + 0.592883i 0 4.00663i 0 0 0
1151.9 0 0 0 1.62081 + 0.935772i 0 2.07786i 0 0 0
1151.10 0 0 0 2.15944 + 1.24676i 0 0.872468i 0 0 0
1151.11 0 0 0 2.27729 + 1.31480i 0 3.01718i 0 0 0
1151.12 0 0 0 3.43403 + 1.98264i 0 2.01359i 0 0 0
2591.1 0 0 0 −3.43403 + 1.98264i 0 2.01359i 0 0 0
2591.2 0 0 0 −2.27729 + 1.31480i 0 3.01718i 0 0 0
2591.3 0 0 0 −2.15944 + 1.24676i 0 0.872468i 0 0 0
2591.4 0 0 0 −1.62081 + 0.935772i 0 2.07786i 0 0 0
2591.5 0 0 0 −1.02690 + 0.592883i 0 4.00663i 0 0 0
2591.6 0 0 0 −0.420258 + 0.242636i 0 1.92619i 0 0 0
2591.7 0 0 0 0.420258 0.242636i 0 1.92619i 0 0 0
2591.8 0 0 0 1.02690 0.592883i 0 4.00663i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1151.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
76.g odd 6 1 inner
228.m even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2736.2.cg.a 24
3.b odd 2 1 inner 2736.2.cg.a 24
4.b odd 2 1 2736.2.cg.b yes 24
12.b even 2 1 2736.2.cg.b yes 24
19.c even 3 1 2736.2.cg.b yes 24
57.h odd 6 1 2736.2.cg.b yes 24
76.g odd 6 1 inner 2736.2.cg.a 24
228.m even 6 1 inner 2736.2.cg.a 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2736.2.cg.a 24 1.a even 1 1 trivial
2736.2.cg.a 24 3.b odd 2 1 inner
2736.2.cg.a 24 76.g odd 6 1 inner
2736.2.cg.a 24 228.m even 6 1 inner
2736.2.cg.b yes 24 4.b odd 2 1
2736.2.cg.b yes 24 12.b even 2 1
2736.2.cg.b yes 24 19.c even 3 1
2736.2.cg.b yes 24 57.h odd 6 1