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Properties

Label 30345.2.a.ck
Level $30345$
Weight $2$
Character orbit 30345.a
Self dual yes
Analytic conductor $242.306$
Dimension $6$

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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] = [30345,2,Mod(1,30345)] 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("30345.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 30345 = 3 \cdot 5 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 30345.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,-2,6,14,6,-2,-6,0,6,-2,-8,14,-4,2,6,18,0,-2,-8,14,-6,2,0,0, 6,-8,6,-14,2,-2,-14,-12,-8,0,-6,14,18,-6,-4,0,-6,2,-18,-56,6,8,-22,18, 6,-2,0,-22,-24,-2,-8,0,-8,-22,-12,14,26,32,-6,14,-4,2,20,0,0,2,-24,0,-14, -34,6,6,8,-8,-28,18,6,-2,-14,-14,0,-42,2,20,18,-2,4,-32,-14,-46,-8,-12, 4,-2,-8,14] 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: \(242.306044934\)
Dimension: \(6\)
Coefficient field: 6.6.933067472.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 11x^{4} + 22x^{3} + 27x^{2} - 58x + 9 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q - 2 q^{2} + 6 q^{3} + 14 q^{4} + 6 q^{5} - 2 q^{6} - 6 q^{7} + 6 q^{9} - 2 q^{10} - 8 q^{11} + 14 q^{12} - 4 q^{13} + 2 q^{14} + 6 q^{15} + 18 q^{16} - 2 q^{18} - 8 q^{19} + 14 q^{20} - 6 q^{21} + 2 q^{22}+ \cdots - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(7\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.