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Properties

Label 10230.2.a.bu
Level $10230$
Weight $2$
Character orbit 10230.a
Self dual yes
Analytic conductor $81.687$
Dimension $3$
CM no
Inner twists $1$

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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] = [10230,2,Mod(1,10230)] 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("10230.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10230 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10230.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-3,3,3,-3,-3,-4,-3,3,3,3,3,6,4,-3,3,2,-3,-4,-3,-4,-3,-8,-3, 3,-6,3,-4,-2,3,-3,-3,3,-2,4,3,-6,4,6,3,-2,4,-16,3,-3,8,12,3,3,-3,2,6,6, -3,-3,4,-4,2,-16,-3,2,3,-4,3,-6,-3,4,2,-8,-4,-4,-3,10,6,3,-4,-4,-6,4,-3, 3,2,4,-4,-2,16,-2,-3,-26,3,-8,-8,-3,-12,4,-3,2,-3,3,3] 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: \(81.6869612678\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} + 4 q^{14} - 3 q^{15} + 3 q^{16} + 2 q^{17} - 3 q^{18} - 4 q^{19} - 3 q^{20}+ \cdots + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(11\) \( -1 \)
\(31\) \( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.