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Properties

Label 2576.2.e.d
Level $2576$
Weight $2$
Character orbit 2576.e
Analytic conductor $20.569$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2576,2,Mod(1471,2576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("2576.1471");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2576 = 2^{4} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2576.e (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: \(20.5694635607\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{7} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{7} - 28 q^{9} + 12 q^{13} + 16 q^{15} + 16 q^{19} - 32 q^{25} - 12 q^{29} + 12 q^{41} + 16 q^{43} + 24 q^{49} - 8 q^{51} - 28 q^{63} - 40 q^{67} + 16 q^{69} - 4 q^{73} + 56 q^{79} + 40 q^{81} - 48 q^{83} + 8 q^{85} + 12 q^{91} - 52 q^{93} + 32 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1471.1 0 − 3.26670i 0 − 2.74761i 0 1.00000 0 −7.67133 0
1471.2 0 − 3.14628i 0 0.761045i 0 1.00000 0 −6.89908 0
1471.3 0 − 2.66763i 0 4.05332i 0 1.00000 0 −4.11625 0
1471.4 0 − 2.62842i 0 0.576269i 0 1.00000 0 −3.90861 0
1471.5 0 − 2.27598i 0 1.75423i 0 1.00000 0 −2.18010 0
1471.6 0 − 1.88340i 0 − 3.43487i 0 1.00000 0 −0.547192 0
1471.7 0 − 1.60731i 0 − 1.45993i 0 1.00000 0 0.416545 0
1471.8 0 − 1.41759i 0 4.35494i 0 1.00000 0 0.990444 0
1471.9 0 − 1.07613i 0 0.430772i 0 1.00000 0 1.84194 0
1471.10 0 − 0.589660i 0 − 2.74543i 0 1.00000 0 2.65230 0
1471.11 0 − 0.573722i 0 2.23847i 0 1.00000 0 2.67084 0
1471.12 0 − 0.499518i 0 1.55038i 0 1.00000 0 2.75048 0
1471.13 0 0.499518i 0 − 1.55038i 0 1.00000 0 2.75048 0
1471.14 0 0.573722i 0 − 2.23847i 0 1.00000 0 2.67084 0
1471.15 0 0.589660i 0 2.74543i 0 1.00000 0 2.65230 0
1471.16 0 1.07613i 0 − 0.430772i 0 1.00000 0 1.84194 0
1471.17 0 1.41759i 0 − 4.35494i 0 1.00000 0 0.990444 0
1471.18 0 1.60731i 0 1.45993i 0 1.00000 0 0.416545 0
1471.19 0 1.88340i 0 3.43487i 0 1.00000 0 −0.547192 0
1471.20 0 2.27598i 0 − 1.75423i 0 1.00000 0 −2.18010 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1471.24
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2576.2.e.d yes 24
4.b odd 2 1 2576.2.e.c ✓ 24
23.b odd 2 1 2576.2.e.c ✓ 24
92.b even 2 1 inner 2576.2.e.d yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2576.2.e.c ✓ 24 4.b odd 2 1
2576.2.e.c ✓ 24 23.b odd 2 1
2576.2.e.d yes 24 1.a even 1 1 trivial
2576.2.e.d yes 24 92.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 \(S_{2}^{\mathrm{new}}(2576, [\chi])\):

\( T_{3}^{24} + 50 T_{3}^{22} + 1069 T_{3}^{20} + 12812 T_{3}^{18} + 94892 T_{3}^{16} + 451952 T_{3}^{14} + \cdots + 16384 \) Copy content Toggle raw display
\( T_{11}^{12} - 68 T_{11}^{10} - 60 T_{11}^{9} + 1604 T_{11}^{8} + 2472 T_{11}^{7} - 14780 T_{11}^{6} + \cdots - 20480 \) Copy content Toggle raw display