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Properties

Label 30912.2.a.db
Level $30912$
Weight $2$
Character orbit 30912.a
Self dual yes
Analytic conductor $246.834$
Dimension $2$

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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] = [30912,2,Mod(1,30912)] 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("30912.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30912, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 30912 = 2^{6} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 30912.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,-2,0,3,0,-2,0,2,0,0,0,7,0,-3,0,-2,0,-12,0,2,0,-2,0,-3,0, -2,0,-8,0,10,0,0,0,-3,0,10,0,-7,0,4,0,-1,0,3,0,-6,0,2,0,2,0,5,0,-5,0,12, 0,-3,0,7,0,-2,0,18,0,-7,0,2,0,-21,0,2,0,3,0,0,0,6,0,2,0,-2,0,7,0,8,0,-17, 0,-7,0,-10,0,-13,0,-12,0,0,0] 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: \(246.833562728\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{5}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q - 2 q^{3} + 3 q^{5} - 2 q^{7} + 2 q^{9} + 7 q^{13} - 3 q^{15} - 2 q^{17} - 12 q^{19} + 2 q^{21} - 2 q^{23} - 3 q^{25} - 2 q^{27} - 8 q^{29} + 10 q^{31} - 3 q^{35} + 10 q^{37} - 7 q^{39} + 4 q^{41} - q^{43}+ \cdots - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(7\) \( +1 \)
\(23\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.