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Properties

Label 48552.2.a.bn
Level $48552$
Weight $2$
Character orbit 48552.a
Self dual yes
Analytic conductor $387.690$
Dimension $2$

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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] = [48552,2,Mod(1,48552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(48552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("48552.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 48552 = 2^{3} \cdot 3 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 48552.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,2,0,3,0,2,0,2,0,-5,0,-1,0,3,0,0,0,-5,0,2,0,-7,0,3,0,2,0, 2,0,2,0,-5,0,3,0,-8,0,-1,0,5,0,3,0,3,0,2,0,2,0,0,0,-8,0,1,0,-5,0,0,0,6, 0,2,0,7,0,-4,0,-7,0,-8,0,4,0,3,0,-5,0,-6,0,2,0,-8,0,0,0,2,0,-26,0,-1,0, 2,0,1,0,2,0,-5,0] 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: \(387.689671894\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{3} + 3 q^{5} + 2 q^{7} + 2 q^{9} - 5 q^{11} - q^{13} + 3 q^{15} - 5 q^{19} + 2 q^{21} - 7 q^{23} + 3 q^{25} + 2 q^{27} + 2 q^{29} + 2 q^{31} - 5 q^{33} + 3 q^{35} - 8 q^{37} - q^{39} + 5 q^{41}+ \cdots - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(7\) \( -1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.