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Properties

Label 3024.2.t.l
Level $3024$
Weight $2$
Character orbit 3024.t
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
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] = [3024,2,Mod(289,3024)]
 
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([0, 0, 4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.t (of order \(3\), 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: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q + 6 q^{5} - 7 q^{7} + 6 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} - 4 q^{23} + 20 q^{25} - 9 q^{29} + 4 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} + 5 q^{47} - 15 q^{49} - 11 q^{53} - 22 q^{55} - 19 q^{59} - 13 q^{61} - 13 q^{65} - 26 q^{67} - 48 q^{71} - 35 q^{73} + 4 q^{77} - 10 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} + 12 q^{95} - 29 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
289.1 0 0 0 −3.84095 0 −0.676469 − 2.55781i 0 0 0
289.2 0 0 0 −2.66802 0 −1.94471 + 1.79391i 0 0 0
289.3 0 0 0 −1.85591 0 2.60465 − 0.464545i 0 0 0
289.4 0 0 0 −1.68316 0 −0.960133 + 2.46539i 0 0 0
289.5 0 0 0 −0.340200 0 −1.09748 − 2.40739i 0 0 0
289.6 0 0 0 0.481387 0 −2.53326 − 0.763277i 0 0 0
289.7 0 0 0 1.58188 0 1.80922 + 1.93047i 0 0 0
289.8 0 0 0 1.83657 0 −2.45061 + 0.997255i 0 0 0
289.9 0 0 0 2.52290 0 1.07705 + 2.41660i 0 0 0
289.10 0 0 0 3.43592 0 1.83889 − 1.90223i 0 0 0
289.11 0 0 0 3.52959 0 −1.16715 − 2.37440i 0 0 0
1873.1 0 0 0 −3.84095 0 −0.676469 + 2.55781i 0 0 0
1873.2 0 0 0 −2.66802 0 −1.94471 − 1.79391i 0 0 0
1873.3 0 0 0 −1.85591 0 2.60465 + 0.464545i 0 0 0
1873.4 0 0 0 −1.68316 0 −0.960133 − 2.46539i 0 0 0
1873.5 0 0 0 −0.340200 0 −1.09748 + 2.40739i 0 0 0
1873.6 0 0 0 0.481387 0 −2.53326 + 0.763277i 0 0 0
1873.7 0 0 0 1.58188 0 1.80922 − 1.93047i 0 0 0
1873.8 0 0 0 1.83657 0 −2.45061 − 0.997255i 0 0 0
1873.9 0 0 0 2.52290 0 1.07705 − 2.41660i 0 0 0
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 289.11
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
63.g even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3024.2.t.l 22
3.b odd 2 1 1008.2.t.k 22
4.b odd 2 1 1512.2.t.d 22
7.c even 3 1 3024.2.q.k 22
9.c even 3 1 3024.2.q.k 22
9.d odd 6 1 1008.2.q.k 22
12.b even 2 1 504.2.t.d yes 22
21.h odd 6 1 1008.2.q.k 22
28.g odd 6 1 1512.2.q.c 22
36.f odd 6 1 1512.2.q.c 22
36.h even 6 1 504.2.q.d ✓ 22
63.g even 3 1 inner 3024.2.t.l 22
63.n odd 6 1 1008.2.t.k 22
84.n even 6 1 504.2.q.d ✓ 22
252.o even 6 1 504.2.t.d yes 22
252.bl odd 6 1 1512.2.t.d 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
504.2.q.d ✓ 22 36.h even 6 1
504.2.q.d ✓ 22 84.n even 6 1
504.2.t.d yes 22 12.b even 2 1
504.2.t.d yes 22 252.o even 6 1
1008.2.q.k 22 9.d odd 6 1
1008.2.q.k 22 21.h odd 6 1
1008.2.t.k 22 3.b odd 2 1
1008.2.t.k 22 63.n odd 6 1
1512.2.q.c 22 28.g odd 6 1
1512.2.q.c 22 36.f odd 6 1
1512.2.t.d 22 4.b odd 2 1
1512.2.t.d 22 252.bl odd 6 1
3024.2.q.k 22 7.c even 3 1
3024.2.q.k 22 9.c even 3 1
3024.2.t.l 22 1.a even 1 1 trivial
3024.2.t.l 22 63.g even 3 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(3024, [\chi])\):

\( T_{5}^{11} - 3 T_{5}^{10} - 28 T_{5}^{9} + 85 T_{5}^{8} + 249 T_{5}^{7} - 766 T_{5}^{6} - 841 T_{5}^{5} + \cdots + 466 \) Copy content Toggle raw display
\( T_{11}^{11} - 3 T_{11}^{10} - 55 T_{11}^{9} + 165 T_{11}^{8} + 915 T_{11}^{7} - 2553 T_{11}^{6} + \cdots + 16812 \) Copy content Toggle raw display