Properties

Label 936.2.h.a
Level $936$
Weight $2$
Character orbit 936.h
Analytic conductor $7.474$
Analytic rank $0$
Dimension $56$
Inner twists $8$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [936,2,Mod(467,936)] 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("936.467"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.47399762919\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 8 q^{10} - 8 q^{16} - 32 q^{22} - 56 q^{25} - 32 q^{40} - 32 q^{43} + 24 q^{49} + 16 q^{52} + 72 q^{64} - 8 q^{82} + 48 q^{88} + 48 q^{91} - 16 q^{94}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
467.1 −1.41300 − 0.0585575i 0 1.99314 + 0.165484i − 2.97522i 0 −3.41768 −2.80662 − 0.350542i 0 −0.174222 + 4.20399i
467.2 −1.41300 − 0.0585575i 0 1.99314 + 0.165484i − 2.97522i 0 3.41768 −2.80662 − 0.350542i 0 −0.174222 + 4.20399i
467.3 −1.41300 + 0.0585575i 0 1.99314 − 0.165484i 2.97522i 0 −3.41768 −2.80662 + 0.350542i 0 −0.174222 − 4.20399i
467.4 −1.41300 + 0.0585575i 0 1.99314 − 0.165484i 2.97522i 0 3.41768 −2.80662 + 0.350542i 0 −0.174222 − 4.20399i
467.5 −1.35634 − 0.400412i 0 1.67934 + 1.08619i 0.444635i 0 −1.89754 −1.84284 − 2.14568i 0 0.178037 − 0.603078i
467.6 −1.35634 − 0.400412i 0 1.67934 + 1.08619i 0.444635i 0 1.89754 −1.84284 − 2.14568i 0 0.178037 − 0.603078i
467.7 −1.35634 + 0.400412i 0 1.67934 − 1.08619i − 0.444635i 0 −1.89754 −1.84284 + 2.14568i 0 0.178037 + 0.603078i
467.8 −1.35634 + 0.400412i 0 1.67934 − 1.08619i − 0.444635i 0 1.89754 −1.84284 + 2.14568i 0 0.178037 + 0.603078i
467.9 −1.08450 − 0.907666i 0 0.352286 + 1.96873i − 3.50905i 0 −1.38148 1.40489 − 2.45485i 0 −3.18504 + 3.80557i
467.10 −1.08450 − 0.907666i 0 0.352286 + 1.96873i − 3.50905i 0 1.38148 1.40489 − 2.45485i 0 −3.18504 + 3.80557i
467.11 −1.08450 + 0.907666i 0 0.352286 − 1.96873i 3.50905i 0 −1.38148 1.40489 + 2.45485i 0 −3.18504 − 3.80557i
467.12 −1.08450 + 0.907666i 0 0.352286 − 1.96873i 3.50905i 0 1.38148 1.40489 + 2.45485i 0 −3.18504 − 3.80557i
467.13 −1.06031 − 0.935815i 0 0.248500 + 1.98450i 1.34579i 0 −4.68994 1.59364 − 2.33673i 0 1.25941 − 1.42695i
467.14 −1.06031 − 0.935815i 0 0.248500 + 1.98450i 1.34579i 0 4.68994 1.59364 − 2.33673i 0 1.25941 − 1.42695i
467.15 −1.06031 + 0.935815i 0 0.248500 − 1.98450i − 1.34579i 0 −4.68994 1.59364 + 2.33673i 0 1.25941 + 1.42695i
467.16 −1.06031 + 0.935815i 0 0.248500 − 1.98450i − 1.34579i 0 4.68994 1.59364 + 2.33673i 0 1.25941 + 1.42695i
467.17 −0.736329 − 1.20740i 0 −0.915638 + 1.77809i 3.67314i 0 −1.90277 2.82108 − 0.203717i 0 4.43495 − 2.70464i
467.18 −0.736329 − 1.20740i 0 −0.915638 + 1.77809i 3.67314i 0 1.90277 2.82108 − 0.203717i 0 4.43495 − 2.70464i
467.19 −0.736329 + 1.20740i 0 −0.915638 − 1.77809i − 3.67314i 0 −1.90277 2.82108 + 0.203717i 0 4.43495 + 2.70464i
467.20 −0.736329 + 1.20740i 0 −0.915638 − 1.77809i − 3.67314i 0 1.90277 2.82108 + 0.203717i 0 4.43495 + 2.70464i
See all 56 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 467.56
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
8.d odd 2 1 inner
13.b even 2 1 inner
24.f even 2 1 inner
39.d odd 2 1 inner
104.h odd 2 1 inner
312.h even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 936.2.h.a ✓ 56
3.b odd 2 1 inner 936.2.h.a ✓ 56
4.b odd 2 1 3744.2.h.a 56
8.b even 2 1 3744.2.h.a 56
8.d odd 2 1 inner 936.2.h.a ✓ 56
12.b even 2 1 3744.2.h.a 56
13.b even 2 1 inner 936.2.h.a ✓ 56
24.f even 2 1 inner 936.2.h.a ✓ 56
24.h odd 2 1 3744.2.h.a 56
39.d odd 2 1 inner 936.2.h.a ✓ 56
52.b odd 2 1 3744.2.h.a 56
104.e even 2 1 3744.2.h.a 56
104.h odd 2 1 inner 936.2.h.a ✓ 56
156.h even 2 1 3744.2.h.a 56
312.b odd 2 1 3744.2.h.a 56
312.h even 2 1 inner 936.2.h.a ✓ 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
936.2.h.a ✓ 56 1.a even 1 1 trivial
936.2.h.a ✓ 56 3.b odd 2 1 inner
936.2.h.a ✓ 56 8.d odd 2 1 inner
936.2.h.a ✓ 56 13.b even 2 1 inner
936.2.h.a ✓ 56 24.f even 2 1 inner
936.2.h.a ✓ 56 39.d odd 2 1 inner
936.2.h.a ✓ 56 104.h odd 2 1 inner
936.2.h.a ✓ 56 312.h even 2 1 inner
3744.2.h.a 56 4.b odd 2 1
3744.2.h.a 56 8.b even 2 1
3744.2.h.a 56 12.b even 2 1
3744.2.h.a 56 24.h odd 2 1
3744.2.h.a 56 52.b odd 2 1
3744.2.h.a 56 104.e even 2 1
3744.2.h.a 56 156.h even 2 1
3744.2.h.a 56 312.b odd 2 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(936, [\chi])\).