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Properties

Label 25410.2.a.bc
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,-1,1,6,-1,8,-1,1,0,-3,-1,1, 1,1,1,3,1,5,-1,0,-6,-1,1,8,-8,-1,1,9,-1,5,0,-1,3,6,1,1,-1,6,-1,6,-1,0, -1,8,-3,3,-1,-1,-5,1,1,1,0,-7,6,-3,1,3,-1,-4,-8,1,8,0,1,8,-1,1,-9,3,1, -6,-5,3,0,3,1,-1,-3,5,-6,-8,-1,8,-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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{12} - q^{13} - q^{14} - q^{15} + q^{16} + 6 q^{17} - q^{18} + 8 q^{19} - q^{20} + q^{21} - 3 q^{23} - q^{24}+ \cdots - q^{98}+O(q^{100}) \) 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.