↑

Properties

Label 232.3.w.b
Level $232$
Weight $3$
Character orbit 232.w
Analytic conductor $6.322$
Analytic rank $0$
Dimension $96$
Inner twists $2$

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] = [232,3,Mod(73,232)] 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("232.73"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(232, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([0, 0, 27])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 232 = 2^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 232.w (of order \(28\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.32154213316\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(8\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 4 q^{3} + 28 q^{5} - 34 q^{7} - 56 q^{11} + 88 q^{15} - 48 q^{17} - 6 q^{19} + 28 q^{21} + 74 q^{23} + 84 q^{25} + 256 q^{27} + 58 q^{29} - 38 q^{31} - 224 q^{33} - 32 q^{37} + 40 q^{39} - 100 q^{41}+ \cdots - 520 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
73.1 0 −3.94476 + 2.47866i 0 6.18277 + 4.93059i 0 −1.10321 + 4.83346i 0 5.51244 − 11.4467i 0
73.2 0 −3.72106 + 2.33809i 0 −6.37393 − 5.08304i 0 0.0264375 − 0.115830i 0 4.47462 − 9.29164i 0
73.3 0 −1.90073 + 1.19431i 0 −0.226049 − 0.180268i 0 1.28945 − 5.64946i 0 −1.71855 + 3.56860i 0
73.4 0 0.0140132 − 0.00880507i 0 −1.20159 − 0.958236i 0 −1.50061 + 6.57460i 0 −3.90483 + 8.10847i 0
73.5 0 0.681268 − 0.428069i 0 4.32797 + 3.45144i 0 2.13004 − 9.33231i 0 −3.62407 + 7.52546i 0
73.6 0 2.42845 − 1.52590i 0 1.80711 + 1.44112i 0 −2.65397 + 11.6278i 0 −0.335935 + 0.697576i 0
73.7 0 3.26806 − 2.05346i 0 −6.16637 − 4.91751i 0 0.209390 − 0.917397i 0 2.55858 − 5.31295i 0
73.8 0 4.66794 − 2.93306i 0 3.95772 + 3.15618i 0 1.29369 − 5.66801i 0 9.28188 − 19.2740i 0
89.1 0 −3.94476 − 2.47866i 0 6.18277 − 4.93059i 0 −1.10321 − 4.83346i 0 5.51244 + 11.4467i 0
89.2 0 −3.72106 − 2.33809i 0 −6.37393 + 5.08304i 0 0.0264375 + 0.115830i 0 4.47462 + 9.29164i 0
89.3 0 −1.90073 − 1.19431i 0 −0.226049 + 0.180268i 0 1.28945 + 5.64946i 0 −1.71855 − 3.56860i 0
89.4 0 0.0140132 + 0.00880507i 0 −1.20159 + 0.958236i 0 −1.50061 − 6.57460i 0 −3.90483 − 8.10847i 0
89.5 0 0.681268 + 0.428069i 0 4.32797 − 3.45144i 0 2.13004 + 9.33231i 0 −3.62407 − 7.52546i 0
89.6 0 2.42845 + 1.52590i 0 1.80711 − 1.44112i 0 −2.65397 − 11.6278i 0 −0.335935 − 0.697576i 0
89.7 0 3.26806 + 2.05346i 0 −6.16637 + 4.91751i 0 0.209390 + 0.917397i 0 2.55858 + 5.31295i 0
89.8 0 4.66794 + 2.93306i 0 3.95772 − 3.15618i 0 1.29369 + 5.66801i 0 9.28188 + 19.2740i 0
97.1 0 −4.31095 − 1.50847i 0 −6.71724 − 1.53317i 0 −4.92282 + 2.37070i 0 9.27236 + 7.39446i 0
97.2 0 −3.92021 − 1.37174i 0 4.91027 + 1.12074i 0 −5.78513 + 2.78597i 0 6.44990 + 5.14362i 0
97.3 0 −2.61400 − 0.914679i 0 −0.902227 − 0.205927i 0 7.60623 − 3.66297i 0 −1.04011 − 0.829461i 0
97.4 0 −1.01259 − 0.354320i 0 8.73493 + 1.99369i 0 2.00268 − 0.964442i 0 −6.13669 − 4.89385i 0
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 73.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.f odd 28 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 232.3.w.b ✓ 96
29.f odd 28 1 inner 232.3.w.b ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
232.3.w.b ✓ 96 1.a even 1 1 trivial
232.3.w.b ✓ 96 29.f odd 28 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{96} - 4 T_{3}^{95} + 8 T_{3}^{94} - 156 T_{3}^{93} - 779 T_{3}^{92} + 6368 T_{3}^{91} + \cdots + 54\!\cdots\!64 \) acting on \(S_{3}^{\mathrm{new}}(232, [\chi])\). Copy content Toggle raw display