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Properties

Label 10470.2.a.m
Level $10470$
Weight $2$
Character orbit 10470.a
Self dual yes
Analytic conductor $83.603$
Dimension $12$
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] = [10470,2,Mod(1,10470)] 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("10470.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10470, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10470 = 2 \cdot 3 \cdot 5 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10470.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,12,-12,12,12,-12,-6,12,12,12,-12,-12,-7,-6,-12,12,-13,12, -12,12,6,-12,-20,-12,12,-7,-12,-6,3,-12,-9,12,12,-13,-6,12,3,-12,7,12, -5,6,-24,-12,12,-20,-34,-12,-4,12,13,-7,-21,-12,-12,-6,12,3,-18,-12,9, -9,-6,12,-7,12,-31,-13,20,-6,-35,12,3,3,-12,-12,-18,7,-35,12,12,-5,-39, 6,-13,-24,-3,-12,0,12,-21,-20,9,-34,-12,-12,-12,-4,-12,12] 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: \(83.6033709163\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} - 15 x^{10} + 60 x^{9} + 86 x^{8} - 298 x^{7} - 250 x^{6} + 538 x^{5} + 368 x^{4} + \cdots - 1 \) 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.

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(349\) \( +1 \)

Inner twists

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

Twists

Twists of this newform have not been computed.