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Properties

Label 5040.2.k.i
Level $5040$
Weight $2$
Character orbit 5040.k
Analytic conductor $40.245$
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] = [5040,2,Mod(1889,5040)] 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("5040.1889"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5040, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5040.k (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(40.2446026187\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 2520)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{23} - 16 q^{25} - 4 q^{35} - 12 q^{49} + 24 q^{53} + 8 q^{65} + 4 q^{77} - 40 q^{79} + 24 q^{85} + 36 q^{91} + 48 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1889.1 0 0 0 −2.22844 − 0.184526i 0 −0.741091 + 2.53984i 0 0 0
1889.2 0 0 0 −2.22844 + 0.184526i 0 −0.741091 − 2.53984i 0 0 0
1889.3 0 0 0 −1.99614 − 1.00769i 0 2.58943 + 0.542983i 0 0 0
1889.4 0 0 0 −1.99614 + 1.00769i 0 2.58943 − 0.542983i 0 0 0
1889.5 0 0 0 −1.52549 − 1.63489i 0 0.114732 − 2.64326i 0 0 0
1889.6 0 0 0 −1.52549 + 1.63489i 0 0.114732 + 2.64326i 0 0 0
1889.7 0 0 0 −0.873162 − 2.05854i 0 −2.52372 − 0.794245i 0 0 0
1889.8 0 0 0 −0.873162 + 2.05854i 0 −2.52372 + 0.794245i 0 0 0
1889.9 0 0 0 −0.727958 − 2.11426i 0 1.21521 + 2.35016i 0 0 0
1889.10 0 0 0 −0.727958 + 2.11426i 0 1.21521 − 2.35016i 0 0 0
1889.11 0 0 0 −0.655755 − 2.13775i 0 −2.09441 + 1.61662i 0 0 0
1889.12 0 0 0 −0.655755 + 2.13775i 0 −2.09441 − 1.61662i 0 0 0
1889.13 0 0 0 0.655755 − 2.13775i 0 2.09441 − 1.61662i 0 0 0
1889.14 0 0 0 0.655755 + 2.13775i 0 2.09441 + 1.61662i 0 0 0
1889.15 0 0 0 0.727958 − 2.11426i 0 −1.21521 − 2.35016i 0 0 0
1889.16 0 0 0 0.727958 + 2.11426i 0 −1.21521 + 2.35016i 0 0 0
1889.17 0 0 0 0.873162 − 2.05854i 0 2.52372 + 0.794245i 0 0 0
1889.18 0 0 0 0.873162 + 2.05854i 0 2.52372 − 0.794245i 0 0 0
1889.19 0 0 0 1.52549 − 1.63489i 0 −0.114732 + 2.64326i 0 0 0
1889.20 0 0 0 1.52549 + 1.63489i 0 −0.114732 − 2.64326i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 1889.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
15.d odd 2 1 inner
105.g even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5040.2.k.i 24
3.b odd 2 1 5040.2.k.h 24
4.b odd 2 1 2520.2.k.a ✓ 24
5.b even 2 1 5040.2.k.h 24
7.b odd 2 1 inner 5040.2.k.i 24
12.b even 2 1 2520.2.k.b yes 24
15.d odd 2 1 inner 5040.2.k.i 24
20.d odd 2 1 2520.2.k.b yes 24
21.c even 2 1 5040.2.k.h 24
28.d even 2 1 2520.2.k.a ✓ 24
35.c odd 2 1 5040.2.k.h 24
60.h even 2 1 2520.2.k.a ✓ 24
84.h odd 2 1 2520.2.k.b yes 24
105.g even 2 1 inner 5040.2.k.i 24
140.c even 2 1 2520.2.k.b yes 24
420.o odd 2 1 2520.2.k.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2520.2.k.a ✓ 24 4.b odd 2 1
2520.2.k.a ✓ 24 28.d even 2 1
2520.2.k.a ✓ 24 60.h even 2 1
2520.2.k.a ✓ 24 420.o odd 2 1
2520.2.k.b yes 24 12.b even 2 1
2520.2.k.b yes 24 20.d odd 2 1
2520.2.k.b yes 24 84.h odd 2 1
2520.2.k.b yes 24 140.c even 2 1
5040.2.k.h 24 3.b odd 2 1
5040.2.k.h 24 5.b even 2 1
5040.2.k.h 24 21.c even 2 1
5040.2.k.h 24 35.c odd 2 1
5040.2.k.i 24 1.a even 1 1 trivial
5040.2.k.i 24 7.b odd 2 1 inner
5040.2.k.i 24 15.d odd 2 1 inner
5040.2.k.i 24 105.g even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(5040, [\chi])\):

\( T_{11}^{12} + 74T_{11}^{10} + 1832T_{11}^{8} + 20176T_{11}^{6} + 103248T_{11}^{4} + 217632T_{11}^{2} + 123904 \) Copy content Toggle raw display
\( T_{13}^{12} - 94T_{13}^{10} + 2680T_{13}^{8} - 21280T_{13}^{6} + 20160T_{13}^{4} - 6016T_{13}^{2} + 512 \) Copy content Toggle raw display
\( T_{23}^{6} - 2T_{23}^{5} - 68T_{23}^{4} + 272T_{23}^{3} + 252T_{23}^{2} - 1736T_{23} + 1312 \) Copy content Toggle raw display