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Properties

Label 13520.2.a.bf
Level $13520$
Weight $2$
Character orbit 13520.a
Self dual yes
Analytic conductor $107.958$
Dimension $1$

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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] = [13520,2,Mod(1,13520)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13520, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("13520.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 13520 = 2^{4} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 13520.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,3,0,1,0,-3,0,6,0,-3,0,0,0,3,0,-7,0,-1,0,-9,0,7,0,1,0,9,0, -5,0,4,0,-9,0,-3,0,-3,0,0,0,7,0,9,0,6,0,-8,0,2,0,-21,0,-6,0,-3,0,-3,0, -5,0,-5,0,-18,0,0,0,-13,0,21,0,3,0,-14,0,3,0,9,0,8,0,9,0,-12,0,-7,0,-15, 0,7,0,0,0,12,0,-1,0,-11,0,-18,0] 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: \(107.957743533\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + 3 q^{3} + q^{5} - 3 q^{7} + 6 q^{9} - 3 q^{11} + 3 q^{15} - 7 q^{17} - q^{19} - 9 q^{21} + 7 q^{23} + q^{25} + 9 q^{27} - 5 q^{29} + 4 q^{31} - 9 q^{33} - 3 q^{35} - 3 q^{37} + 7 q^{41} + 9 q^{43}+ \cdots - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.