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Properties

Label 8024.2.a.bb
Level $8024$
Weight $2$
Character orbit 8024.a
Self dual yes
Analytic conductor $64.072$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8024,2,Mod(1,8024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8024.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8024.a (trivial)

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: yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 8 q^{5} - 3 q^{7} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 8 q^{5} - 3 q^{7} + 40 q^{9} + 3 q^{11} + 13 q^{13} + 4 q^{15} + 32 q^{17} + 14 q^{19} - 7 q^{21} + 7 q^{23} + 38 q^{25} + 9 q^{27} + 17 q^{29} + 15 q^{31} + 18 q^{33} + 6 q^{35} + 21 q^{37} + 16 q^{39} + 49 q^{41} - 7 q^{43} + 14 q^{45} - 25 q^{47} + 37 q^{49} + 12 q^{53} + 15 q^{55} + 45 q^{57} + 32 q^{59} + 5 q^{61} - 12 q^{63} + 39 q^{65} + 12 q^{69} - 13 q^{71} + 70 q^{73} - 47 q^{75} - 10 q^{77} - q^{79} + 84 q^{81} - 17 q^{83} + 8 q^{85} + 20 q^{87} + 42 q^{89} + 36 q^{91} + 2 q^{93} - q^{95} + 58 q^{97} + 7 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 0 −3.16628 0 −1.06664 0 −0.836052 0 7.02534 0
1.2 0 −3.01806 0 3.78696 0 −1.07498 0 6.10866 0
1.3 0 −2.97402 0 −3.33527 0 3.60888 0 5.84478 0
1.4 0 −2.96706 0 3.51833 0 3.62712 0 5.80344 0
1.5 0 −2.65698 0 −1.37353 0 −4.51033 0 4.05953 0
1.6 0 −2.35639 0 1.88610 0 −3.68573 0 2.55257 0
1.7 0 −2.29360 0 −3.85032 0 1.95004 0 2.26061 0
1.8 0 −2.23251 0 3.10540 0 −3.44467 0 1.98408 0
1.9 0 −1.67764 0 −0.206110 0 −1.52712 0 −0.185517 0
1.10 0 −1.26190 0 1.28218 0 −0.0440837 0 −1.40761 0
1.11 0 −1.21753 0 0.238125 0 5.25396 0 −1.51763 0
1.12 0 −1.11553 0 −3.13935 0 0.425117 0 −1.75560 0
1.13 0 −0.551342 0 0.616724 0 1.02317 0 −2.69602 0
1.14 0 −0.394982 0 −0.737434 0 −1.31966 0 −2.84399 0
1.15 0 −0.321300 0 3.25819 0 3.32621 0 −2.89677 0
1.16 0 −0.159636 0 −1.22368 0 3.18149 0 −2.97452 0
1.17 0 0.0290013 0 3.75701 0 −1.56335 0 −2.99916 0
1.18 0 0.147881 0 −3.84317 0 −0.153864 0 −2.97813 0
1.19 0 0.792010 0 −0.983575 0 1.99855 0 −2.37272 0
1.20 0 0.804465 0 3.90815 0 3.10524 0 −2.35284 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.32
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(17\) \(-1\)
\(59\) \(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 8024.2.a.bb ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8024.2.a.bb ✓ 32 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):

\( T_{3}^{32} - 68 T_{3}^{30} - 3 T_{3}^{29} + 2057 T_{3}^{28} + 163 T_{3}^{27} - 36519 T_{3}^{26} + \cdots + 1152 \) Copy content Toggle raw display
\( T_{5}^{32} - 8 T_{5}^{31} - 67 T_{5}^{30} + 658 T_{5}^{29} + 1751 T_{5}^{28} - 23833 T_{5}^{27} + \cdots - 3207168 \) Copy content Toggle raw display
\( T_{7}^{32} + 3 T_{7}^{31} - 126 T_{7}^{30} - 375 T_{7}^{29} + 7013 T_{7}^{28} + 20576 T_{7}^{27} + \cdots - 82313216 \) Copy content Toggle raw display