↑

Properties

Label 13475.2.a.c
Level $13475$
Weight $2$
Character orbit 13475.a
Self dual yes
Analytic conductor $107.598$
Dimension $1$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [13475,2,Mod(1,13475)] 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("13475.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13475, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 13475 = 5^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 13475.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,-1,0,0,0,3,-3,0,-1,0,2,0,0,-1,6,3,4,0,0,1,-4,0,0,-2,0, 0,6,0,8,-5,0,-6,0,3,2,-4,0,0,-2,0,-4,1,0,4,-12,0,0,0,0,-2,2,0,0,0,0,-6, -4,0,10,-8,0,7,0,0,16,-6,0,0,8,-9,14,-2,0,-4,0,0,8,0,9,2,-4,0,0,4,0,-3, -10,0,0,4,0,12,0,0,10,0,3,0] 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: \(107.598416724\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{4} + 3 q^{8} - 3 q^{9} - q^{11} + 2 q^{13} - q^{16} + 6 q^{17} + 3 q^{18} + 4 q^{19} + q^{22} - 4 q^{23} - 2 q^{26} + 6 q^{29} + 8 q^{31} - 5 q^{32} - 6 q^{34} + 3 q^{36} + 2 q^{37}+ \cdots + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(5\) \( +1 \)
\(7\) \( -1 \)
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.