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Properties

Label 19663.2.a.o
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,-3,-3,39,-12,0,-39,-9,42,-6,3,-6,0,3,-3,39,-3,24,9,-72,3, -30,-6,0,39,12,-78,-39,12,-6,-12,-21,-24,-24,12,-3,-6,18,90,3,-42,0,0, 9,-33,0,-30,57,39,3,-9,-18,0,-36,-60,9,-42,-18,27,150,-3,-75,-42,39,9, 45,-12,45,-42,6,0,39,-75,-141,-66,48,-3,-45,45,-6,147,63,-54,6,-18,-9, -45,-75,-9,15,0,-108,36,-48,-24,-18,6,-3,3,27] 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.

\(\operatorname{Tr}(f)(q) = \) \( 39 q - 3 q^{2} - 3 q^{3} + 39 q^{4} - 12 q^{5} - 39 q^{7} - 9 q^{8} + 42 q^{9} - 6 q^{10} + 3 q^{11} - 6 q^{12} + 3 q^{14} - 3 q^{15} + 39 q^{16} - 3 q^{17} + 24 q^{18} + 9 q^{19} - 72 q^{20} + 3 q^{21}+ \cdots + 3 q^{99}+O(q^{100}) \) 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.