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Properties

Label 46410.2.a.ck
Level $46410$
Weight $2$
Character orbit 46410.a
Self dual yes
Analytic conductor $370.586$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [46410,2,Mod(1,46410)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(46410, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("46410.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 46410 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 46410.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(370.585715781\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + q^{10} - 4 q^{11} + q^{12} + q^{13} - q^{14} + q^{15} + q^{16} + q^{17} + q^{18} + 4 q^{19} + q^{20} - q^{21} - 4 q^{22} + 8 q^{23} + q^{24} + q^{25} + q^{26} + q^{27} - q^{28} - 2 q^{29} + q^{30} + q^{32} - 4 q^{33} + q^{34} - q^{35} + q^{36} + 6 q^{37} + 4 q^{38} + q^{39} + q^{40} + 10 q^{41} - q^{42} - 4 q^{43} - 4 q^{44} + q^{45} + 8 q^{46} + q^{48} + q^{49} + q^{50} + q^{51} + q^{52} - 10 q^{53} + q^{54} - 4 q^{55} - q^{56} + 4 q^{57} - 2 q^{58} - 4 q^{59} + q^{60} - 2 q^{61} - q^{63} + q^{64} + q^{65} - 4 q^{66} + 4 q^{67} + q^{68} + 8 q^{69} - q^{70} + 8 q^{71} + q^{72} + 10 q^{73} + 6 q^{74} + q^{75} + 4 q^{76} + 4 q^{77} + q^{78} - 16 q^{79} + q^{80} + q^{81} + 10 q^{82} - 12 q^{83} - q^{84} + q^{85} - 4 q^{86} - 2 q^{87} - 4 q^{88} + 10 q^{89} + q^{90} - q^{91} + 8 q^{92} + 4 q^{95} + q^{96} + 2 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( -1 \)
\(7\) \( +1 \)
\(13\) \( -1 \)
\(17\) \( -1 \)

Inner twists

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

Twists

Twists of this newform have not been computed.