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Properties

Label 10005.2.a.s
Level $10005$
Weight $2$
Character orbit 10005.a
Self dual yes
Analytic conductor $79.890$
Dimension $18$
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] = [10005,2,Mod(1,10005)] 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("10005.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10005, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10005 = 3 \cdot 5 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10005.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [18,-5,18,13,18,-5,-24,-12,18,-5,-12,13,-9,-4,18,7,-8,-5,-25, 13,-24,11,18,-12,18,3,18,-25,18,-5,-23,-14,-12,-27,-24,13,-32,-35,-9,-12, -24,-4,-16,-23,18,-5,-40,7,4,-5,-8,-13,-17,-5,-12,20,-25,-5,-37,13,-17, -40,-24,-48,-9,11,-46,1,18,-4,-20,-12,7,13,18,-6,0,3,21,7,18,22,-26,-25, -8,2,18,-36,-40,-5,-40,13,-23,8,-25,-14,-18,-8,-12,13] 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: \(79.8903272223\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 5 x^{17} - 12 x^{16} + 91 x^{15} + 16 x^{14} - 644 x^{13} + 352 x^{12} + 2231 x^{11} + \cdots + 15 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 18 q - 5 q^{2} + 18 q^{3} + 13 q^{4} + 18 q^{5} - 5 q^{6} - 24 q^{7} - 12 q^{8} + 18 q^{9} - 5 q^{10} - 12 q^{11} + 13 q^{12} - 9 q^{13} - 4 q^{14} + 18 q^{15} + 7 q^{16} - 8 q^{17} - 5 q^{18} - 25 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(23\) \( -1 \)
\(29\) \( -1 \)

Inner twists

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

Twists

Twists of this newform have not been computed.