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Properties

Label 3024.2.cc.d
Level $3024$
Weight $2$
Character orbit 3024.cc
Analytic conductor $24.147$
Analytic rank $0$
Dimension $48$
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(881,3024)]
 
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, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.cc (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: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
881.1 0 0 0 −1.91834 + 3.32266i 0 −2.41978 − 1.06989i 0 0 0
881.2 0 0 0 −1.79302 + 3.10561i 0 −2.25543 + 1.38312i 0 0 0
881.3 0 0 0 −1.79123 + 3.10250i 0 2.56863 − 0.634134i 0 0 0
881.4 0 0 0 −1.60290 + 2.77631i 0 0.555071 + 2.58687i 0 0 0
881.5 0 0 0 −1.26858 + 2.19724i 0 −0.521158 − 2.59391i 0 0 0
881.6 0 0 0 −1.16173 + 2.01217i 0 1.39373 + 2.24889i 0 0 0
881.7 0 0 0 −1.11364 + 1.92889i 0 2.58429 − 0.566975i 0 0 0
881.8 0 0 0 −0.965651 + 1.67256i 0 −2.53170 + 0.768427i 0 0 0
881.9 0 0 0 −0.422480 + 0.731757i 0 −0.327684 − 2.62538i 0 0 0
881.10 0 0 0 −0.0977451 + 0.169300i 0 2.48762 + 0.900962i 0 0 0
881.11 0 0 0 −0.0868503 + 0.150429i 0 −1.72196 + 2.00869i 0 0 0
881.12 0 0 0 −0.00869840 + 0.0150661i 0 0.514871 − 2.59517i 0 0 0
881.13 0 0 0 0.00869840 − 0.0150661i 0 −2.50492 − 0.851694i 0 0 0
881.14 0 0 0 0.0868503 − 0.150429i 0 2.60056 − 0.486915i 0 0 0
881.15 0 0 0 0.0977451 − 0.169300i 0 −0.463555 + 2.60483i 0 0 0
881.16 0 0 0 0.422480 − 0.731757i 0 −2.10980 − 1.59647i 0 0 0
881.17 0 0 0 0.965651 − 1.67256i 0 1.93133 − 1.80831i 0 0 0
881.18 0 0 0 1.11364 − 1.92889i 0 −1.78316 + 1.95457i 0 0 0
881.19 0 0 0 1.16173 − 2.01217i 0 1.25073 + 2.33145i 0 0 0
881.20 0 0 0 1.26858 − 2.19724i 0 −1.98582 − 1.74829i 0 0 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 881.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
9.d odd 6 1 inner
63.o 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.cc.d 48
3.b odd 2 1 1008.2.cc.d 48
4.b odd 2 1 1512.2.bu.a 48
7.b odd 2 1 inner 3024.2.cc.d 48
9.c even 3 1 1008.2.cc.d 48
9.d odd 6 1 inner 3024.2.cc.d 48
12.b even 2 1 504.2.bu.a ✓ 48
21.c even 2 1 1008.2.cc.d 48
28.d even 2 1 1512.2.bu.a 48
36.f odd 6 1 504.2.bu.a ✓ 48
36.f odd 6 1 4536.2.k.a 48
36.h even 6 1 1512.2.bu.a 48
36.h even 6 1 4536.2.k.a 48
63.l odd 6 1 1008.2.cc.d 48
63.o even 6 1 inner 3024.2.cc.d 48
84.h odd 2 1 504.2.bu.a ✓ 48
252.s odd 6 1 1512.2.bu.a 48
252.s odd 6 1 4536.2.k.a 48
252.bi even 6 1 504.2.bu.a ✓ 48
252.bi even 6 1 4536.2.k.a 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
504.2.bu.a ✓ 48 12.b even 2 1
504.2.bu.a ✓ 48 36.f odd 6 1
504.2.bu.a ✓ 48 84.h odd 2 1
504.2.bu.a ✓ 48 252.bi even 6 1
1008.2.cc.d 48 3.b odd 2 1
1008.2.cc.d 48 9.c even 3 1
1008.2.cc.d 48 21.c even 2 1
1008.2.cc.d 48 63.l odd 6 1
1512.2.bu.a 48 4.b odd 2 1
1512.2.bu.a 48 28.d even 2 1
1512.2.bu.a 48 36.h even 6 1
1512.2.bu.a 48 252.s odd 6 1
3024.2.cc.d 48 1.a even 1 1 trivial
3024.2.cc.d 48 7.b odd 2 1 inner
3024.2.cc.d 48 9.d odd 6 1 inner
3024.2.cc.d 48 63.o even 6 1 inner
4536.2.k.a 48 36.f odd 6 1
4536.2.k.a 48 36.h even 6 1
4536.2.k.a 48 252.s odd 6 1
4536.2.k.a 48 252.bi even 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{48} + 72 T_{5}^{46} + 2973 T_{5}^{44} + 83564 T_{5}^{42} + 1771392 T_{5}^{40} + 29379510 T_{5}^{38} + \cdots + 16 \) acting on \(S_{2}^{\mathrm{new}}(3024, [\chi])\). Copy content Toggle raw display