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Properties

Label 2520.2.k.b
Level $2520$
Weight $2$
Character orbit 2520.k
Analytic conductor $20.122$
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] = [2520,2,Mod(1889,2520)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2520, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2520.1889");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.k (of order \(2\), degree \(1\), 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: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{23} - 16 q^{25} - 4 q^{35} - 12 q^{49} - 24 q^{53} - 8 q^{65} - 4 q^{77} + 40 q^{79} + 24 q^{85} - 36 q^{91} + 48 q^{95}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
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 990-1000
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 2520.2.k.b yes 24
3.b odd 2 1 2520.2.k.a ✓ 24
4.b odd 2 1 5040.2.k.h 24
5.b even 2 1 2520.2.k.a ✓ 24
7.b odd 2 1 inner 2520.2.k.b yes 24
12.b even 2 1 5040.2.k.i 24
15.d odd 2 1 inner 2520.2.k.b yes 24
20.d odd 2 1 5040.2.k.i 24
21.c even 2 1 2520.2.k.a ✓ 24
28.d even 2 1 5040.2.k.h 24
35.c odd 2 1 2520.2.k.a ✓ 24
60.h even 2 1 5040.2.k.h 24
84.h odd 2 1 5040.2.k.i 24
105.g even 2 1 inner 2520.2.k.b yes 24
140.c even 2 1 5040.2.k.i 24
420.o odd 2 1 5040.2.k.h 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2520.2.k.a ✓ 24 3.b odd 2 1
2520.2.k.a ✓ 24 5.b even 2 1
2520.2.k.a ✓ 24 21.c even 2 1
2520.2.k.a ✓ 24 35.c odd 2 1
2520.2.k.b yes 24 1.a even 1 1 trivial
2520.2.k.b yes 24 7.b odd 2 1 inner
2520.2.k.b yes 24 15.d odd 2 1 inner
2520.2.k.b yes 24 105.g even 2 1 inner
5040.2.k.h 24 4.b odd 2 1
5040.2.k.h 24 28.d even 2 1
5040.2.k.h 24 60.h even 2 1
5040.2.k.h 24 420.o odd 2 1
5040.2.k.i 24 12.b even 2 1
5040.2.k.i 24 20.d odd 2 1
5040.2.k.i 24 84.h odd 2 1
5040.2.k.i 24 140.c even 2 1