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Properties

Label 5819.2.a.t
Level $5819$
Weight $2$
Character orbit 5819.a
Self dual yes
Analytic conductor $46.465$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 5819 = 11 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5819.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [60,5,9,73,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(46.4649489362\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: no (minimal twist has level 253)
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.

\(\operatorname{Tr}(f)(q) = \) \( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} - 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} + 7 q^{10} - 60 q^{11} + 41 q^{12} + 46 q^{13} - 16 q^{14} - 4 q^{15} + 99 q^{16} + 5 q^{17} + 36 q^{18} + 8 q^{19} - 82 q^{20}+ \cdots - 75 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.79615 −1.84647 5.81843 −3.71917 5.16301 1.39957 −10.6769 0.409465 10.3993
1.2 −2.75068 2.41262 5.56624 −0.502504 −6.63634 4.38344 −9.80957 2.82073 1.38223
1.3 −2.61042 0.301187 4.81428 −0.335914 −0.786224 3.57653 −7.34645 −2.90929 0.876875
1.4 −2.56762 −1.86277 4.59270 −2.06282 4.78289 −4.15023 −6.65707 0.469907 5.29655
1.5 −2.53611 1.73986 4.43185 −3.67453 −4.41248 −2.39766 −6.16743 0.0271203 9.31902
1.6 −2.40987 0.529518 3.80746 1.55984 −1.27607 −3.57353 −4.35574 −2.71961 −3.75900
1.7 −2.29534 −3.02840 3.26860 −1.86081 6.95122 4.83491 −2.91187 6.17120 4.27120
1.8 −2.18618 −0.281561 2.77937 3.34100 0.615543 0.567189 −1.70384 −2.92072 −7.30402
1.9 −2.14004 3.21406 2.57978 −3.86980 −6.87822 3.08033 −1.24075 7.33017 8.28154
1.10 −2.05610 −2.21869 2.22755 4.33173 4.56186 −2.89005 −0.467865 1.92260 −8.90647
1.11 −2.03269 1.07604 2.13185 −0.410257 −2.18727 −4.26763 −0.268004 −1.84213 0.833927
1.12 −1.77899 −1.88973 1.16479 −1.17802 3.36180 1.47227 1.48583 0.571076 2.09569
1.13 −1.67053 3.39922 0.790674 1.45882 −5.67850 1.59098 2.02022 8.55467 −2.43701
1.14 −1.66144 −1.56821 0.760370 0.618995 2.60547 −1.60957 2.05957 −0.540729 −1.02842
1.15 −1.45488 0.314839 0.116668 −4.22769 −0.458053 −1.05551 2.74002 −2.90088 6.15076
1.16 −1.41986 −1.33152 0.0159886 3.46743 1.89056 4.25485 2.81701 −1.22706 −4.92324
1.17 −1.39808 1.29637 −0.0453613 1.63900 −1.81244 2.62653 2.85959 −1.31942 −2.29147
1.18 −1.37192 −3.24389 −0.117831 −1.23015 4.45036 −3.99271 2.90550 7.52280 1.68767
1.19 −1.22583 1.22479 −0.497336 −2.74249 −1.50139 4.85150 3.06131 −1.49988 3.36183
1.20 −1.12774 2.11139 −0.728194 −0.943998 −2.38110 −1.55399 3.07670 1.45795 1.06459
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.60
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(11\) \( +1 \)
\(23\) \( -1 \)

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 5819.2.a.t 60
23.b odd 2 1 5819.2.a.u 60
23.d odd 22 2 253.2.i.b ✓ 120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
253.2.i.b ✓ 120 23.d odd 22 2
5819.2.a.t 60 1.a even 1 1 trivial
5819.2.a.u 60 23.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5819))\):

\( T_{2}^{60} - 5 T_{2}^{59} - 84 T_{2}^{58} + 445 T_{2}^{57} + 3305 T_{2}^{56} - 18701 T_{2}^{55} + \cdots + 314368 \) Copy content Toggle raw display
\( T_{5}^{60} + 8 T_{5}^{59} - 166 T_{5}^{58} - 1478 T_{5}^{57} + 12447 T_{5}^{56} + 127574 T_{5}^{55} + \cdots + 175036061908861 \) Copy content Toggle raw display