↑

Properties

Label 30345.2.a.cm
Level $30345$
Weight $2$
Character orbit 30345.a
Self dual yes
Analytic conductor $242.306$
Dimension $6$

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] = [30345,2,Mod(1,30345)] 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("30345.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 30345 = 3 \cdot 5 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 30345.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,-1,6,9,-6,-1,6,6,6,1,-2,9,-3,-1,-6,11,0,-1,-9,-9,6,11,11,6, 6,6,6,9,14,1,0,46,-2,0,-6,9,-5,-10,-3,-6,-4,-1,5,-1,-6,5,16,11,6,-1,0, 35,-17,-1,2,6,-9,10,-9,-9,-17,5,6,34,3,11,0,0,11,1,28,6,23,-17,6,4,-2, 6,-4,-11,6,-46,8,9,0,12,14,24,-30,1,-3,-13,0,-27,9,46,5,-1,-2,9] 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: \(242.306044934\)
Dimension: \(6\)
Coefficient field: 6.6.61882489.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 10x^{4} + 11x^{3} + 21x^{2} - 17x - 9 \) Copy content Toggle raw display
Twist minimal: not computed
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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q - q^{2} + 6 q^{3} + 9 q^{4} - 6 q^{5} - q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + q^{10} - 2 q^{11} + 9 q^{12} - 3 q^{13} - q^{14} - 6 q^{15} + 11 q^{16} - q^{18} - 9 q^{19} - 9 q^{20} + 6 q^{21} + 11 q^{22}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.