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Properties

Label 3024.2.ch.c
Level $3024$
Weight $2$
Character orbit 3024.ch
Analytic conductor $24.147$
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] = [3024,2,Mod(575,3024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.575");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.ch (of order \(6\), degree \(2\), 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: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 1008)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 12 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 12 q^{5} + 24 q^{25} - 36 q^{29} + 24 q^{37} + 36 q^{41} + 12 q^{49} + 36 q^{65} + 24 q^{73} - 12 q^{85}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
575.1 0 0 0 −3.58692 + 2.07091i 0 0.866025 + 0.500000i 0 0 0
575.2 0 0 0 −3.58692 + 2.07091i 0 −0.866025 − 0.500000i 0 0 0
575.3 0 0 0 −1.03368 + 0.596793i 0 −0.866025 − 0.500000i 0 0 0
575.4 0 0 0 −1.03368 + 0.596793i 0 0.866025 + 0.500000i 0 0 0
575.5 0 0 0 1.05527 − 0.609261i 0 −0.866025 − 0.500000i 0 0 0
575.6 0 0 0 1.05527 − 0.609261i 0 0.866025 + 0.500000i 0 0 0
575.7 0 0 0 1.38379 − 0.798929i 0 −0.866025 − 0.500000i 0 0 0
575.8 0 0 0 1.38379 − 0.798929i 0 0.866025 + 0.500000i 0 0 0
575.9 0 0 0 1.84481 − 1.06510i 0 0.866025 + 0.500000i 0 0 0
575.10 0 0 0 1.84481 − 1.06510i 0 −0.866025 − 0.500000i 0 0 0
575.11 0 0 0 3.33673 − 1.92646i 0 −0.866025 − 0.500000i 0 0 0
575.12 0 0 0 3.33673 − 1.92646i 0 0.866025 + 0.500000i 0 0 0
1583.1 0 0 0 −3.58692 − 2.07091i 0 0.866025 − 0.500000i 0 0 0
1583.2 0 0 0 −3.58692 − 2.07091i 0 −0.866025 + 0.500000i 0 0 0
1583.3 0 0 0 −1.03368 − 0.596793i 0 −0.866025 + 0.500000i 0 0 0
1583.4 0 0 0 −1.03368 − 0.596793i 0 0.866025 − 0.500000i 0 0 0
1583.5 0 0 0 1.05527 + 0.609261i 0 −0.866025 + 0.500000i 0 0 0
1583.6 0 0 0 1.05527 + 0.609261i 0 0.866025 − 0.500000i 0 0 0
1583.7 0 0 0 1.38379 + 0.798929i 0 −0.866025 + 0.500000i 0 0 0
1583.8 0 0 0 1.38379 + 0.798929i 0 0.866025 − 0.500000i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 575.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
9.d odd 6 1 inner
36.h even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3024.2.ch.c 24
3.b odd 2 1 1008.2.ch.b ✓ 24
4.b odd 2 1 inner 3024.2.ch.c 24
9.c even 3 1 1008.2.ch.b ✓ 24
9.d odd 6 1 inner 3024.2.ch.c 24
12.b even 2 1 1008.2.ch.b ✓ 24
36.f odd 6 1 1008.2.ch.b ✓ 24
36.h even 6 1 inner 3024.2.ch.c 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1008.2.ch.b ✓ 24 3.b odd 2 1
1008.2.ch.b ✓ 24 9.c even 3 1
1008.2.ch.b ✓ 24 12.b even 2 1
1008.2.ch.b ✓ 24 36.f odd 6 1
3024.2.ch.c 24 1.a even 1 1 trivial
3024.2.ch.c 24 4.b odd 2 1 inner
3024.2.ch.c 24 9.d odd 6 1 inner
3024.2.ch.c 24 36.h even 6 1 inner