Properties

Label 10470.2.a.p
Level $10470$
Weight $2$
Character orbit 10470.a
Self dual yes
Analytic conductor $83.603$
Dimension $14$
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 = [14,-14,-14,14,14,14,5,-14,14,-14,-6,-14,9,-5,-14,14,16,-14,-11, 14,-5,6,4,14,14,-9,-14,5,8,14,-28,-14,6,-16,5,14,19,11,-9,-14,8,5,-9,-6, 14,-4,18,-14,9,-14,-16,9,36,14,-6,-5,11,-8,10,-14,-17,28,5,14,9,-6,8,16, -4,-5,-3,-14,-3,-19,-14,-11,52,9,-28,14,14,-8,43,-5,16,9,-8,6,21,-14,-29, 4,28,-18,-11,14,20,-9,-6,14] 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: \(83.6033709163\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - x^{13} - 47 x^{12} + 91 x^{11} + 563 x^{10} - 1349 x^{9} - 1832 x^{8} + 5026 x^{7} + 2158 x^{6} + \cdots + 2 \) 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.

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