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Properties

Label 19663.2.a.n
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.