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Properties

Label 92.5.c.a
Level $92$
Weight $5$
Character orbit 92.c
Analytic conductor $9.510$
Analytic rank $0$
Dimension $44$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [92,5,Mod(47,92)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(92, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("92.47");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 92.c (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(9.51003660371\)
Analytic rank: \(0\)
Dimension: \(44\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
47.1 −3.90902 − 0.848274i 16.4740i 14.5609 + 6.63184i −40.3079 13.9745 − 64.3971i 75.6184i −51.2931 − 38.2756i −190.392 157.564 + 34.1921i
47.2 −3.90902 + 0.848274i − 16.4740i 14.5609 − 6.63184i −40.3079 13.9745 + 64.3971i − 75.6184i −51.2931 + 38.2756i −190.392 157.564 − 34.1921i
47.3 −3.78901 − 1.28195i 8.06260i 12.7132 + 9.71463i 47.7328 10.3358 − 30.5493i 53.2079i −35.7169 − 53.1065i 15.9945 −180.860 − 61.1909i
47.4 −3.78901 + 1.28195i − 8.06260i 12.7132 − 9.71463i 47.7328 10.3358 + 30.5493i − 53.2079i −35.7169 + 53.1065i 15.9945 −180.860 + 61.1909i
47.5 −3.73586 − 1.42945i − 15.9813i 11.9134 + 10.6804i 10.8136 −22.8444 + 59.7040i 78.4065i −29.2396 − 56.9302i −174.403 −40.3982 − 15.4575i
47.6 −3.73586 + 1.42945i 15.9813i 11.9134 − 10.6804i 10.8136 −22.8444 − 59.7040i − 78.4065i −29.2396 + 56.9302i −174.403 −40.3982 + 15.4575i
47.7 −3.67495 − 1.57947i − 5.27417i 11.0105 + 11.6090i −2.28864 −8.33042 + 19.3823i − 11.6647i −22.1271 − 60.0532i 53.1831 8.41065 + 3.61485i
47.8 −3.67495 + 1.57947i 5.27417i 11.0105 − 11.6090i −2.28864 −8.33042 − 19.3823i 11.6647i −22.1271 + 60.0532i 53.1831 8.41065 − 3.61485i
47.9 −3.38026 − 2.13866i 9.77702i 6.85227 + 14.4584i 5.72766 20.9097 − 33.0488i − 87.3864i 7.75923 − 63.5279i −14.5900 −19.3610 − 12.2495i
47.10 −3.38026 + 2.13866i − 9.77702i 6.85227 − 14.4584i 5.72766 20.9097 + 33.0488i 87.3864i 7.75923 + 63.5279i −14.5900 −19.3610 + 12.2495i
47.11 −2.62123 − 3.02145i − 11.5336i −2.25832 + 15.8398i 21.9613 −34.8483 + 30.2323i − 69.4040i 53.7788 − 34.6964i −52.0244 −57.5657 − 66.3551i
47.12 −2.62123 + 3.02145i 11.5336i −2.25832 − 15.8398i 21.9613 −34.8483 − 30.2323i 69.4040i 53.7788 + 34.6964i −52.0244 −57.5657 + 66.3551i
47.13 −2.57175 − 3.06367i − 5.48369i −2.77216 + 15.7580i −44.5238 −16.8002 + 14.1027i 30.2349i 55.4067 − 32.0328i 50.9292 114.504 + 136.406i
47.14 −2.57175 + 3.06367i 5.48369i −2.77216 − 15.7580i −44.5238 −16.8002 − 14.1027i − 30.2349i 55.4067 + 32.0328i 50.9292 114.504 − 136.406i
47.15 −2.20274 − 3.33885i 10.3499i −6.29588 + 14.7092i −0.915094 34.5567 − 22.7981i 20.9067i 62.9802 − 11.3796i −26.1201 2.01571 + 3.05537i
47.16 −2.20274 + 3.33885i − 10.3499i −6.29588 − 14.7092i −0.915094 34.5567 + 22.7981i − 20.9067i 62.9802 + 11.3796i −26.1201 2.01571 − 3.05537i
47.17 −1.24134 − 3.80251i − 3.60489i −12.9181 + 9.44044i 30.7683 −13.7076 + 4.47491i 33.9778i 51.9332 + 37.4025i 68.0048 −38.1940 − 116.997i
47.18 −1.24134 + 3.80251i 3.60489i −12.9181 − 9.44044i 30.7683 −13.7076 − 4.47491i − 33.9778i 51.9332 − 37.4025i 68.0048 −38.1940 + 116.997i
47.19 −0.491879 − 3.96964i 10.1341i −15.5161 + 3.90516i −20.8818 40.2287 − 4.98474i − 26.1126i 23.1341 + 59.6725i −21.6999 10.2713 + 82.8932i
47.20 −0.491879 + 3.96964i − 10.1341i −15.5161 − 3.90516i −20.8818 40.2287 + 4.98474i 26.1126i 23.1341 − 59.6725i −21.6999 10.2713 − 82.8932i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 47.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 92.5.c.a ✓ 44
4.b odd 2 1 inner 92.5.c.a ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
92.5.c.a ✓ 44 1.a even 1 1 trivial
92.5.c.a ✓ 44 4.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(92, [\chi])\).