↑

Properties

Label 25410.2.a.fg
Level $25410$
Weight $2$
Character orbit 25410.a
Self dual yes
Analytic conductor $202.900$
Dimension $4$

Related objects

Downloads

Learn more

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,-2,-4,-4,4,-2,4,4,4,4,0,-4,-4,4, -2,-4,-4,2,-4,-4,4,0,-2,-4,4,-4,4,2,4,0,4,-6,0,4,-4,4,-4,4,4,2,-2,-8,-4, 0,-4,-4,2,-12,-4,-18,-4,-4,4,-2,0,-10,-2,4,-4,-22,4,-14,-4,-4,4,0,2,20, 4,4,0,8,4,-2,-6,-2,0,-42,4,2,-4,4,4,4,-4,4,4,0,4] 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: 4.4.25488.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 9x^{2} - 6x + 6 \) 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.

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