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Properties

Label 2736.2.cg.c
Level $2736$
Weight $2$
Character orbit 2736.cg
Analytic conductor $21.847$
Analytic rank $0$
Dimension $32$
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] = [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: \(32\)
Relative dimension: \(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 16 q^{13} + 24 q^{25} - 16 q^{37} - 96 q^{49} - 8 q^{61} - 8 q^{73} + 16 q^{85} + 48 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1151.1 0 0 0 −3.37787 − 1.95021i 0 3.27561i 0 0 0
1151.2 0 0 0 −3.37787 − 1.95021i 0 − 3.27561i 0 0 0
1151.3 0 0 0 −2.03864 − 1.17701i 0 − 4.52875i 0 0 0
1151.4 0 0 0 −2.03864 − 1.17701i 0 4.52875i 0 0 0
1151.5 0 0 0 −1.45856 − 0.842100i 0 0.172239i 0 0 0
1151.6 0 0 0 −1.45856 − 0.842100i 0 − 0.172239i 0 0 0
1151.7 0 0 0 −1.34408 − 0.776006i 0 − 2.95486i 0 0 0
1151.8 0 0 0 −1.34408 − 0.776006i 0 2.95486i 0 0 0
1151.9 0 0 0 1.34408 + 0.776006i 0 − 2.95486i 0 0 0
1151.10 0 0 0 1.34408 + 0.776006i 0 2.95486i 0 0 0
1151.11 0 0 0 1.45856 + 0.842100i 0 0.172239i 0 0 0
1151.12 0 0 0 1.45856 + 0.842100i 0 − 0.172239i 0 0 0
1151.13 0 0 0 2.03864 + 1.17701i 0 − 4.52875i 0 0 0
1151.14 0 0 0 2.03864 + 1.17701i 0 4.52875i 0 0 0
1151.15 0 0 0 3.37787 + 1.95021i 0 3.27561i 0 0 0
1151.16 0 0 0 3.37787 + 1.95021i 0 − 3.27561i 0 0 0
2591.1 0 0 0 −3.37787 + 1.95021i 0 − 3.27561i 0 0 0
2591.2 0 0 0 −3.37787 + 1.95021i 0 3.27561i 0 0 0
2591.3 0 0 0 −2.03864 + 1.17701i 0 4.52875i 0 0 0
2591.4 0 0 0 −2.03864 + 1.17701i 0 − 4.52875i 0 0 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1151.16
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
12.b even 2 1 inner
19.c even 3 1 inner
57.h odd 6 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.c ✓ 32
3.b odd 2 1 inner 2736.2.cg.c ✓ 32
4.b odd 2 1 inner 2736.2.cg.c ✓ 32
12.b even 2 1 inner 2736.2.cg.c ✓ 32
19.c even 3 1 inner 2736.2.cg.c ✓ 32
57.h odd 6 1 inner 2736.2.cg.c ✓ 32
76.g odd 6 1 inner 2736.2.cg.c ✓ 32
228.m even 6 1 inner 2736.2.cg.c ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2736.2.cg.c ✓ 32 1.a even 1 1 trivial
2736.2.cg.c ✓ 32 3.b odd 2 1 inner
2736.2.cg.c ✓ 32 4.b odd 2 1 inner
2736.2.cg.c ✓ 32 12.b even 2 1 inner
2736.2.cg.c ✓ 32 19.c even 3 1 inner
2736.2.cg.c ✓ 32 57.h odd 6 1 inner
2736.2.cg.c ✓ 32 76.g odd 6 1 inner
2736.2.cg.c ✓ 32 228.m even 6 1 inner