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Properties

Label 19663.2.a.q
Level $19663$
Weight $2$
Character orbit 19663.a
Self dual yes
Analytic conductor $157.010$
Dimension $39$

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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] = [19663,2,Mod(1,19663)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19663.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19663, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 19663 = 7 \cdot 53^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 19663.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [39,9,3,39,12,0,39,27,42,30,3,6,0,9,9,39,3,60,21,72,3,-6,30,0, 39,48,72,39,-12,18,12,63,12,0,12,105,6,42,30,75,42,0,0,9,33,36,6,-75,39, 39,15,18,0,42,60,27,-66,30,21,-126,3,-75,42,39,81,45,36,-15,-78,30,72, 147,57,171,-42,36,3,-45,45,144,-45,-9,30,6,6,-9,-39,-3,9,159,0,-12,60, -60,60,-18,6,9,51,111] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(157.009845494\)
Dimension: \(39\)
Twist minimal: not computed
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.

\(\operatorname{Tr}(f)(q) = \) \( 39 q + 9 q^{2} + 3 q^{3} + 39 q^{4} + 12 q^{5} + 39 q^{7} + 27 q^{8} + 42 q^{9} + 30 q^{10} + 3 q^{11} + 6 q^{12} + 9 q^{14} + 9 q^{15} + 39 q^{16} + 3 q^{17} + 60 q^{18} + 21 q^{19} + 72 q^{20} + 3 q^{21}+ \cdots + 51 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(7\) \( -1 \)
\(53\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.