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Properties

Label 16245.2.a.be
Level $16245$
Weight $2$
Character orbit 16245.a
Self dual yes
Analytic conductor $129.717$
Dimension $3$

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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] = [16245,2,Mod(1,16245)] 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("16245.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 16245 = 3^{2} \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16245.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-1,0,7,3,0,2,6,0,-1,5,0,-15,-7,0,3,-1,0,0,7,0,-8,-4,0,3,5, 0,11,2,0,-1,6,0,-25,2,0,-2,0,0,6,2,0,-1,18,0,-24,-6,0,-7,-1,0,-35,-11, 0,5,-15,0,-7,-6,0,-9,13,0,-8,-15,0,-20,-34,0,-7,29,0,-22,7,0,0,16,0,-24, 3,0,31,3,0,-1,32,0,-9,14,0,-10,-41,0,21,0,0,7,-23,0,7] 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: \(129.716978084\)
Dimension: \(3\)
Coefficient field: 3.3.361.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 6x + 7 \) Copy content Toggle raw display
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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - q^{2} + 7 q^{4} + 3 q^{5} + 2 q^{7} + 6 q^{8} - q^{10} + 5 q^{11} - 15 q^{13} - 7 q^{14} + 3 q^{16} - q^{17} + 7 q^{20} - 8 q^{22} - 4 q^{23} + 3 q^{25} + 5 q^{26} + 11 q^{28} + 2 q^{29} - q^{31}+ \cdots - 23 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.