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Properties

Label 23670.2.a.br
Level $23670$
Weight $2$
Character orbit 23670.a
Self dual yes
Analytic conductor $189.006$
Dimension $4$

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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] = [23670,2,Mod(1,23670)] 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("23670.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23670, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 23670 = 2 \cdot 3^{2} \cdot 5 \cdot 263 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 23670.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,4,0,4,-4,0,-9,4,0,-4,3,0,-7,-9,0,4,6,0,4,-4,0,3,-6,0,4,-7, 0,-9,11,0,12,4,0,6,9,0,-17,4,0,-4,0,0,-7,3,0,-6,-8,0,5,4,0,-7,21,0,-3, -9,0,11,-19,0,-1,12,0,4,7,0,-2,6,0,9,-34,0,-3,-17,0,4,-3,0,4,-4,0,0,23, 0,-6,-7,0,3,-7,0,20,-6,0,-8,-4,0,3,5,0,4] 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: \(189.005901584\)
Dimension: \(4\)
Coefficient field: 4.4.8468.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 5x^{2} + 3x + 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q + 4 q^{2} + 4 q^{4} - 4 q^{5} - 9 q^{7} + 4 q^{8} - 4 q^{10} + 3 q^{11} - 7 q^{13} - 9 q^{14} + 4 q^{16} + 6 q^{17} + 4 q^{19} - 4 q^{20} + 3 q^{22} - 6 q^{23} + 4 q^{25} - 7 q^{26} - 9 q^{28} + 11 q^{29}+ \cdots + 5 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(263\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.