↑

Properties

Label 21675.2.a.x
Level $21675$
Weight $2$
Character orbit 21675.a
Self dual yes
Analytic conductor $173.076$
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] = [21675,2,Mod(1,21675)] 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("21675.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(21675, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 21675 = 3 \cdot 5^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 21675.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,2,-1,2,0,-2,1,0,1,0,-2,-2,7,2,0,-4,0,2,3,0,-1,-4,-6,0,0,14, -1,2,-6,0,7,-8,2,0,0,2,2,6,-7,0,-4,-2,-1,-4,0,-12,-6,4,-6,0,0,14,-8,-2, 0,0,-3,-12,-10,0,5,14,1,-8,0,4,-5,0,6,0,-4,0,-14,4,0,6,-2,-14,8,0,1,-8, 14,-2,0,-2,6,0,-12,0,7,-12,-7,-12,0,8,5,-12,-2,0] 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: \(173.075746381\)
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)
 
\(f(q)\) \(=\) \( q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{6} + q^{7} + q^{9} - 2 q^{11} - 2 q^{12} + 7 q^{13} + 2 q^{14} - 4 q^{16} + 2 q^{18} + 3 q^{19} - q^{21} - 4 q^{22} - 6 q^{23} + 14 q^{26} - q^{27} + 2 q^{28}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.