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Properties

Label 529.4.a.l
Level $529$
Weight $4$
Character orbit 529.a
Self dual yes
Analytic conductor $31.212$
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] = [529,4,Mod(1,529)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(529, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("529.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 529 = 23^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 529.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: \(31.2120103930\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{2} + 24 q^{3} + 112 q^{4} - 12 q^{6} + 24 q^{8} + 228 q^{9} + 444 q^{12} - 4 q^{13} + 720 q^{16} + 404 q^{18} + 1332 q^{24} + 800 q^{25} + 372 q^{26} + 1152 q^{27} + 752 q^{29} - 224 q^{31}+ \cdots + 656 q^{98}+O(q^{100}) \) 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.

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 −5.18273 −0.934501 18.8607 −7.90805 4.84327 17.4062 −56.2881 −26.1267 40.9853
1.2 −5.18273 −0.934501 18.8607 7.90805 4.84327 −17.4062 −56.2881 −26.1267 −40.9853
1.3 −4.78413 9.28484 14.8879 −11.1627 −44.4198 −12.0979 −32.9524 59.2083 53.4036
1.4 −4.78413 9.28484 14.8879 11.1627 −44.4198 12.0979 −32.9524 59.2083 −53.4036
1.5 −3.49874 −4.75964 4.24120 −6.95940 16.6528 −9.95165 13.1511 −4.34581 24.3491
1.6 −3.49874 −4.75964 4.24120 6.95940 16.6528 9.95165 13.1511 −4.34581 −24.3491
1.7 −2.02425 −2.87466 −3.90243 −12.2605 5.81902 33.3107 24.0934 −18.7363 24.8182
1.8 −2.02425 −2.87466 −3.90243 12.2605 5.81902 −33.3107 24.0934 −18.7363 −24.8182
1.9 −1.45684 7.83065 −5.87761 −1.67357 −11.4080 −32.2680 20.2175 34.3191 2.43813
1.10 −1.45684 7.83065 −5.87761 1.67357 −11.4080 32.2680 20.2175 34.3191 −2.43813
1.11 0.467470 −0.443481 −7.78147 −16.9623 −0.207314 3.65525 −7.37736 −26.8033 −7.92935
1.12 0.467470 −0.443481 −7.78147 16.9623 −0.207314 −3.65525 −7.37736 −26.8033 7.92935
1.13 1.26033 7.25401 −6.41157 −18.6981 9.14243 −13.1556 −18.1633 25.6207 −23.5658
1.14 1.26033 7.25401 −6.41157 18.6981 9.14243 13.1556 −18.1633 25.6207 23.5658
1.15 1.99819 −0.476116 −4.00725 −16.7765 −0.951368 −10.3260 −23.9927 −26.7733 −33.5226
1.16 1.99819 −0.476116 −4.00725 16.7765 −0.951368 10.3260 −23.9927 −26.7733 33.5226
1.17 3.16637 −8.06841 2.02592 −10.4025 −25.5476 26.5887 −18.9162 38.0992 −32.9383
1.18 3.16637 −8.06841 2.02592 10.4025 −25.5476 −26.5887 −18.9162 38.0992 32.9383
1.19 3.50216 −7.39575 4.26516 −17.4329 −25.9011 −31.4793 −13.0800 27.6972 −61.0529
1.20 3.50216 −7.39575 4.26516 17.4329 −25.9011 31.4793 −13.0800 27.6972 61.0529
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(23\) \( +1 \)

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 529.4.a.l ✓ 24
23.b odd 2 1 inner 529.4.a.l ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
529.4.a.l ✓ 24 1.a even 1 1 trivial
529.4.a.l ✓ 24 23.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(529))\):

\( T_{2}^{12} - 4 T_{2}^{11} - 68 T_{2}^{10} + 268 T_{2}^{9} + 1582 T_{2}^{8} - 6244 T_{2}^{7} + \cdots - 92928 \) Copy content Toggle raw display
\( T_{3}^{12} - 12 T_{3}^{11} - 147 T_{3}^{10} + 1932 T_{3}^{9} + 7344 T_{3}^{8} - 106572 T_{3}^{7} + \cdots - 3079712 \) Copy content Toggle raw display
\( T_{5}^{24} - 1900 T_{5}^{22} + 1578637 T_{5}^{20} - 755197280 T_{5}^{18} + 230609593306 T_{5}^{16} + \cdots + 92\!\cdots\!64 \) Copy content Toggle raw display