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Properties

Label 30912.2.a.dx
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 = [2,0,2,0,1,0,2,0,2,0,0,0,-5,0,1,0,0,0,2,0,2,0,2,0,11,0,2,0,-7, 0,-12,0,0,0,1,0,-1,0,-5,0,9,0,5,0,1,0,-1,0,2,0,0,0,-6,0,0,0,2,0,-14,0, -20,0,2,0,-23,0,8,0,2,0,-2,0,2,0,11,0,0,0,0,0,2,0,-18,0,0,0,-7,0,-18,0, -5,0,-12,0,-40,0,17,0,0,0] 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: \(\Q(\sqrt{41}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 10 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{3} + q^{5} + 2 q^{7} + 2 q^{9} - 5 q^{13} + q^{15} + 2 q^{19} + 2 q^{21} + 2 q^{23} + 11 q^{25} + 2 q^{27} - 7 q^{29} - 12 q^{31} + q^{35} - q^{37} - 5 q^{39} + 9 q^{41} + 5 q^{43} + q^{45}+ \cdots + 17 q^{97}+O(q^{100}) \) 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.