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Properties

Label 25410.2.a.ce
Level $25410$
Weight $2$
Character orbit 25410.a
Self dual yes
Analytic conductor $202.900$
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] = [25410,2,Mod(1,25410)] 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("25410.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25410, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 25410 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 25410.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,1,1,-1,1,1,1,1,0,-1,-1,1,-1,1,-2,1,6,1,-1,0,-7,-1,1,-1, -1,1,1,-1,3,1,0,-2,1,1,0,6,1,1,-9,-1,-1,0,1,-7,8,-1,1,1,2,-1,-6,-1,0,1, -6,1,-11,-1,-3,3,1,1,-1,0,-7,-2,7,1,-15,1,-12,0,-1,6,0,1,6,1,1,-9,-11, -1,-2,-1,-1,0,7,1,-1,-7,-3,8,6,-1,-2,1,0,1] 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: \(202.899871536\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - q^{12} - q^{13} + q^{14} - q^{15} + q^{16} - 2 q^{17} + q^{18} + 6 q^{19} + q^{20} - q^{21} - 7 q^{23} - q^{24}+ \cdots + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(7\) \( -1 \)
\(11\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.