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Properties

Label 42237.2.a.dg
Level $42237$
Weight $2$
Character orbit 42237.a
Self dual yes
Analytic conductor $337.264$
Dimension $30$

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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] = [42237,2,Mod(1,42237)] 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("42237.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42237, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 42237 = 3^{2} \cdot 13 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 42237.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [30,3,0,39,-3,0,18,6,0,-9,0,0,-30,15,0,57,18,0,0,-33,0,-18,45, 0,57,-3,0,24,42,0,-48,-15,0,-30,3,0,-30,0,0,-36,63,0,42,-30,0,-9,12,0, 54,27,0,-39,24,0,0,75,0,-6,12,0,18,66,0,72,3,0,-3,51,0,12,21,0,45,78,0, 0,24,0,-3,-42,0,-42,-12,0,51,36,0,-63,66,0,-18,60,0,-66,0,0,-60,15,0,-6] 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: \(337.264143017\)
Dimension: \(30\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 30 q + 3 q^{2} + 39 q^{4} - 3 q^{5} + 18 q^{7} + 6 q^{8} - 9 q^{10} - 30 q^{13} + 15 q^{14} + 57 q^{16} + 18 q^{17} - 33 q^{20} - 18 q^{22} + 45 q^{23} + 57 q^{25} - 3 q^{26} + 24 q^{28} + 42 q^{29} - 48 q^{31}+ \cdots + 15 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(13\) \( +1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.