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Properties

Label 5780.2.c.j
Level $5780$
Weight $2$
Character orbit 5780.c
Analytic conductor $46.154$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5780,2,Mod(5201,5780)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5780, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5780.5201");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5780 = 2^{2} \cdot 5 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5780.c (of order \(2\), degree \(1\), 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: \(46.1535323683\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 340)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{9} + 16 q^{13} - 32 q^{21} - 24 q^{25} + 16 q^{35} - 16 q^{43} + 16 q^{47} - 40 q^{49} - 32 q^{53} - 16 q^{59} + 32 q^{67} - 32 q^{69} - 48 q^{77} + 8 q^{81} - 64 q^{83} - 32 q^{87} - 16 q^{89} + 16 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5201.1 0 − 3.27990i 0 1.00000i 0 − 4.39608i 0 −7.75771 0
5201.2 0 − 2.89366i 0 − 1.00000i 0 − 3.07222i 0 −5.37326 0
5201.3 0 − 2.68860i 0 − 1.00000i 0 − 1.08148i 0 −4.22856 0
5201.4 0 − 2.41635i 0 1.00000i 0 0.733789i 0 −2.83875 0
5201.5 0 − 2.27331i 0 − 1.00000i 0 2.37337i 0 −2.16796 0
5201.6 0 − 1.96743i 0 1.00000i 0 − 4.13403i 0 −0.870795 0
5201.7 0 − 1.70227i 0 − 1.00000i 0 4.39180i 0 0.102270 0
5201.8 0 − 1.47256i 0 1.00000i 0 1.27134i 0 0.831572 0
5201.9 0 − 0.833172i 0 − 1.00000i 0 1.87711i 0 2.30582 0
5201.10 0 − 0.815249i 0 1.00000i 0 2.85898i 0 2.33537 0
5201.11 0 − 0.567193i 0 1.00000i 0 − 2.93861i 0 2.67829 0
5201.12 0 − 0.127664i 0 − 1.00000i 0 − 3.09319i 0 2.98370 0
5201.13 0 0.127664i 0 1.00000i 0 3.09319i 0 2.98370 0
5201.14 0 0.567193i 0 − 1.00000i 0 2.93861i 0 2.67829 0
5201.15 0 0.815249i 0 − 1.00000i 0 − 2.85898i 0 2.33537 0
5201.16 0 0.833172i 0 1.00000i 0 − 1.87711i 0 2.30582 0
5201.17 0 1.47256i 0 − 1.00000i 0 − 1.27134i 0 0.831572 0
5201.18 0 1.70227i 0 1.00000i 0 − 4.39180i 0 0.102270 0
5201.19 0 1.96743i 0 − 1.00000i 0 4.13403i 0 −0.870795 0
5201.20 0 2.27331i 0 1.00000i 0 − 2.37337i 0 −2.16796 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5201.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5780.2.c.j 24
17.b even 2 1 inner 5780.2.c.j 24
17.c even 4 1 5780.2.a.q 12
17.c even 4 1 5780.2.a.r 12
17.e odd 16 2 340.2.u.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
340.2.u.a ✓ 24 17.e odd 16 2
5780.2.a.q 12 17.c even 4 1
5780.2.a.r 12 17.c even 4 1
5780.2.c.j 24 1.a even 1 1 trivial
5780.2.c.j 24 17.b 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 \(S_{2}^{\mathrm{new}}(5780, [\chi])\):

\( T_{3}^{24} + 48 T_{3}^{22} + 988 T_{3}^{20} + 11440 T_{3}^{18} + 82136 T_{3}^{16} + 379992 T_{3}^{14} + \cdots + 1156 \) Copy content Toggle raw display
\( T_{7}^{24} + 104 T_{7}^{22} + 4704 T_{7}^{20} + 121768 T_{7}^{18} + 1998004 T_{7}^{16} + \cdots + 820364164 \) Copy content Toggle raw display
\( T_{11}^{24} + 120 T_{11}^{22} + 5740 T_{11}^{20} + 144680 T_{11}^{18} + 2129348 T_{11}^{16} + \cdots + 97732996 \) Copy content Toggle raw display