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Properties

Label 3024.2.cx.j
Level $3024$
Weight $2$
Character orbit 3024.cx
Analytic conductor $24.147$
Analytic rank $0$
Dimension $24$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [3024,2,Mod(559,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.559"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4, 3])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.cx (of order \(6\), degree \(2\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,0,0,0,6,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content 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 algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 6 q^{7} + 18 q^{23} + 24 q^{25} + 6 q^{29} - 12 q^{37} - 42 q^{43} + 12 q^{49} - 96 q^{53} - 42 q^{65} - 36 q^{67} + 18 q^{77} + 60 q^{79} - 6 q^{85} - 126 q^{95}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
559.1 0 0 0 −3.48918 + 2.01448i 0 1.90020 + 1.84099i 0 0 0
559.2 0 0 0 −3.37919 + 1.95098i 0 −2.55088 + 0.702155i 0 0 0
559.3 0 0 0 −2.10269 + 1.21399i 0 1.48800 − 2.18766i 0 0 0
559.4 0 0 0 −1.72020 + 0.993161i 0 −1.81723 − 1.92293i 0 0 0
559.5 0 0 0 −0.675942 + 0.390255i 0 1.89912 − 1.84210i 0 0 0
559.6 0 0 0 −0.263424 + 0.152088i 0 2.36807 + 1.17993i 0 0 0
559.7 0 0 0 0.263424 − 0.152088i 0 2.20588 + 1.46085i 0 0 0
559.8 0 0 0 0.675942 − 0.390255i 0 −0.645750 + 2.56574i 0 0 0
559.9 0 0 0 1.72020 − 0.993161i 0 −2.57392 − 0.612306i 0 0 0
559.10 0 0 0 2.10269 − 1.21399i 0 −1.15057 + 2.38247i 0 0 0
559.11 0 0 0 3.37919 − 1.95098i 0 −0.667355 − 2.56020i 0 0 0
559.12 0 0 0 3.48918 − 2.01448i 0 2.54444 + 0.725126i 0 0 0
2575.1 0 0 0 −3.48918 − 2.01448i 0 1.90020 − 1.84099i 0 0 0
2575.2 0 0 0 −3.37919 − 1.95098i 0 −2.55088 − 0.702155i 0 0 0
2575.3 0 0 0 −2.10269 − 1.21399i 0 1.48800 + 2.18766i 0 0 0
2575.4 0 0 0 −1.72020 − 0.993161i 0 −1.81723 + 1.92293i 0 0 0
2575.5 0 0 0 −0.675942 − 0.390255i 0 1.89912 + 1.84210i 0 0 0
2575.6 0 0 0 −0.263424 − 0.152088i 0 2.36807 − 1.17993i 0 0 0
2575.7 0 0 0 0.263424 + 0.152088i 0 2.20588 − 1.46085i 0 0 0
2575.8 0 0 0 0.675942 + 0.390255i 0 −0.645750 − 2.56574i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 559.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
36.f odd 6 1 inner
252.bi 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.cx.j 24
3.b odd 2 1 1008.2.cx.j yes 24
4.b odd 2 1 3024.2.cx.i 24
7.b odd 2 1 inner 3024.2.cx.j 24
9.c even 3 1 3024.2.cx.i 24
9.d odd 6 1 1008.2.cx.i ✓ 24
12.b even 2 1 1008.2.cx.i ✓ 24
21.c even 2 1 1008.2.cx.j yes 24
28.d even 2 1 3024.2.cx.i 24
36.f odd 6 1 inner 3024.2.cx.j 24
36.h even 6 1 1008.2.cx.j yes 24
63.l odd 6 1 3024.2.cx.i 24
63.o even 6 1 1008.2.cx.i ✓ 24
84.h odd 2 1 1008.2.cx.i ✓ 24
252.s odd 6 1 1008.2.cx.j yes 24
252.bi even 6 1 inner 3024.2.cx.j 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1008.2.cx.i ✓ 24 9.d odd 6 1
1008.2.cx.i ✓ 24 12.b even 2 1
1008.2.cx.i ✓ 24 63.o even 6 1
1008.2.cx.i ✓ 24 84.h odd 2 1
1008.2.cx.j yes 24 3.b odd 2 1
1008.2.cx.j yes 24 21.c even 2 1
1008.2.cx.j yes 24 36.h even 6 1
1008.2.cx.j yes 24 252.s odd 6 1
3024.2.cx.i 24 4.b odd 2 1
3024.2.cx.i 24 9.c even 3 1
3024.2.cx.i 24 28.d even 2 1
3024.2.cx.i 24 63.l odd 6 1
3024.2.cx.j 24 1.a even 1 1 trivial
3024.2.cx.j 24 7.b odd 2 1 inner
3024.2.cx.j 24 36.f odd 6 1 inner
3024.2.cx.j 24 252.bi even 6 1 inner

Hecke kernels

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

\( T_{5}^{24} - 42 T_{5}^{22} + 1155 T_{5}^{20} - 18432 T_{5}^{18} + 212814 T_{5}^{16} - 1508085 T_{5}^{14} + \cdots + 104976 \) Copy content Toggle raw display
\( T_{11}^{12} - 42 T_{11}^{10} + 1455 T_{11}^{8} - 81 T_{11}^{7} - 12627 T_{11}^{6} + 2781 T_{11}^{5} + \cdots + 26244 \) Copy content Toggle raw display