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Properties

Label 25410.2.a.fi
Level $25410$
Weight $2$
Character orbit 25410.a
Self dual yes
Analytic conductor $202.900$
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] = [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 = [4,4,4,4,-4,4,-4,4,4,-4,0,4,-1,-4,-4,4,-5,4,-2,-4,-4,0,2,4,4, -1,4,-4,-15,-4,7,4,0,-5,4,4,-5,-2,-1,-4,-3,-4,-5,0,-4,2,1,4,4,4,-5,-1, 17,4,0,-4,-2,-15,-1,-4,-33,7,-4,4,1,0,7,-5,2,4,-5,4,-21,-5,4,-2,0,-1,-2, -4,4,-3,-8,-4,5,-5,-15,0,-27,-4,1,2,7,1,2,4,5,4,0,4] 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: \(4\)
Coefficient field: 4.4.8525.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 8x^{2} + 9x + 19 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{12} - q^{13} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 5 q^{17} + 4 q^{18} - 2 q^{19} - 4 q^{20} - 4 q^{21}+ \cdots + 4 q^{98}+O(q^{100}) \) 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.