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Properties

Label 13552.2.a.dd
Level $13552$
Weight $2$
Character orbit 13552.a
Self dual yes
Analytic conductor $108.213$
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] = [13552,2,Mod(1,13552)] 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("13552.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 13552 = 2^{4} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 13552.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,2,0,-6,0,4,0,-6,0,0,0,0,0,-3,0,-3,0,-3,0,2,0,8,0,0,0,-4, 0,3,0,3,0,0,0,-6,0,-7,0,-5,0,4,0,-8,0,9,0,14,0,4,0,11,0,-9,0,0,0,6,0,25, 0,-19,0,-6,0,12,0,15,0,14,0,7,0,-11,0,5,0,0,0,-8,0,-4,0,1,0,15,0,-6,0, -17,0,0,0,-11,0,-17,0,-15,0,0,0] 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: \(108.213264819\)
Dimension: \(4\)
Coefficient field: 4.4.2525.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 4x^{2} + 5x + 5 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q + 2 q^{3} - 6 q^{5} + 4 q^{7} - 6 q^{9} - 3 q^{15} - 3 q^{17} - 3 q^{19} + 2 q^{21} + 8 q^{23} - 4 q^{27} + 3 q^{29} + 3 q^{31} - 6 q^{35} - 7 q^{37} - 5 q^{39} + 4 q^{41} - 8 q^{43} + 9 q^{45} + 14 q^{47}+ \cdots - 15 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(7\) \( -1 \)
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.