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Properties

Label 10003.2.a.d
Level $10003$
Weight $2$
Character orbit 10003.a
Self dual yes
Analytic conductor $79.874$
Dimension $178$
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] = [10003,2,Mod(1,10003)] 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("10003.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10003, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10003 = 7 \cdot 1429 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10003.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [178,20,14,178,53,23,-178,54,180,26,-36,56,60,-20,3,174,84,59, 27,106,-14,11,20,63,207,53,65,-178,76,14,36,133,54,26,-53,175,88,68,13, 69,124,-23,-9,-13,150,17,90,135,178,64,-57,122,80,103,25,-54,86,10,92, 21,101,112,-180,176,89,32,-21,218,77,-26,-39,170,99,14,86,67,36,44,-7, 203,186,80,119,-56,104,-19,107,-6,105,131,-60,99,118,81,21,211,112,20, -113,240] 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: \(79.8743571419\)
Dimension: \(178\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 178 q + 20 q^{2} + 14 q^{3} + 178 q^{4} + 53 q^{5} + 23 q^{6} - 178 q^{7} + 54 q^{8} + 180 q^{9} + 26 q^{10} - 36 q^{11} + 56 q^{12} + 60 q^{13} - 20 q^{14} + 3 q^{15} + 174 q^{16} + 84 q^{17} + 59 q^{18}+ \cdots - 113 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(7\) \( +1 \)
\(1429\) \( -1 \)

Inner twists

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

Twists

Twists of this newform have not been computed.