Properties

Label 92.10.b.c
Level $92$
Weight $10$
Character orbit 92.b
Analytic conductor $47.383$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [92,10,Mod(91,92)]
 
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, 1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("92.91");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 92.b (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: \(47.3832969271\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 100 q + 32 q^{2} - 856 q^{4} + 12080 q^{6} - 44920 q^{8} - 551128 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 100 q + 32 q^{2} - 856 q^{4} + 12080 q^{6} - 44920 q^{8} - 551128 q^{9} - 266288 q^{12} - 4 q^{13} + 251152 q^{16} - 3213936 q^{18} - 1616600 q^{24} - 50000004 q^{25} - 9377960 q^{26} + 2611028 q^{29} - 1326128 q^{32} - 46192944 q^{36} - 3633996 q^{41} + 117081608 q^{46} + 403873120 q^{48} + 817907260 q^{49} - 253720248 q^{50} - 181337560 q^{52} - 432447896 q^{54} + 29270048 q^{58} + 897716584 q^{62} - 379488256 q^{64} + 8977204 q^{69} - 810209096 q^{70} + 390187056 q^{72} - 4 q^{73} - 413720696 q^{77} + 769707392 q^{78} + 2942959780 q^{81} + 3918346912 q^{82} - 911342216 q^{85} - 1806222144 q^{92} + 8161391316 q^{93} - 2542324232 q^{94} - 1019589584 q^{96} - 911301448 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
91.1 −22.5638 1.69576i 66.5026i 506.249 + 76.5257i 1801.05i −112.773 + 1500.55i 4087.65 −11293.1 2585.19i 15260.4 −3054.15 + 40638.4i
91.2 −22.5638 1.69576i 66.5026i 506.249 + 76.5257i 1801.05i −112.773 + 1500.55i −4087.65 −11293.1 2585.19i 15260.4 3054.15 40638.4i
91.3 −22.5638 + 1.69576i 66.5026i 506.249 76.5257i 1801.05i −112.773 1500.55i −4087.65 −11293.1 + 2585.19i 15260.4 3054.15 + 40638.4i
91.4 −22.5638 + 1.69576i 66.5026i 506.249 76.5257i 1801.05i −112.773 1500.55i 4087.65 −11293.1 + 2585.19i 15260.4 −3054.15 40638.4i
91.5 −22.5102 2.30032i 230.553i 501.417 + 103.561i 660.081i 530.348 5189.80i −9465.28 −11048.8 3484.61i −33471.9 −1518.40 + 14858.6i
91.6 −22.5102 2.30032i 230.553i 501.417 + 103.561i 660.081i 530.348 5189.80i 9465.28 −11048.8 3484.61i −33471.9 1518.40 14858.6i
91.7 −22.5102 + 2.30032i 230.553i 501.417 103.561i 660.081i 530.348 + 5189.80i 9465.28 −11048.8 + 3484.61i −33471.9 1518.40 + 14858.6i
91.8 −22.5102 + 2.30032i 230.553i 501.417 103.561i 660.081i 530.348 + 5189.80i −9465.28 −11048.8 + 3484.61i −33471.9 −1518.40 14858.6i
91.9 −20.8820 8.71446i 73.2819i 360.116 + 363.951i 1060.89i 638.612 1530.27i 7324.58 −4348.32 10738.2i 14312.8 −9245.13 + 22153.6i
91.10 −20.8820 8.71446i 73.2819i 360.116 + 363.951i 1060.89i 638.612 1530.27i −7324.58 −4348.32 10738.2i 14312.8 9245.13 22153.6i
91.11 −20.8820 + 8.71446i 73.2819i 360.116 363.951i 1060.89i 638.612 + 1530.27i −7324.58 −4348.32 + 10738.2i 14312.8 9245.13 + 22153.6i
91.12 −20.8820 + 8.71446i 73.2819i 360.116 363.951i 1060.89i 638.612 + 1530.27i 7324.58 −4348.32 + 10738.2i 14312.8 −9245.13 22153.6i
91.13 −20.1734 10.2486i 108.291i 301.934 + 413.497i 580.393i −1109.82 + 2184.60i −6232.00 −1853.30 11436.0i 7956.11 −5948.19 + 11708.5i
91.14 −20.1734 10.2486i 108.291i 301.934 + 413.497i 580.393i −1109.82 + 2184.60i 6232.00 −1853.30 11436.0i 7956.11 5948.19 11708.5i
91.15 −20.1734 + 10.2486i 108.291i 301.934 413.497i 580.393i −1109.82 2184.60i 6232.00 −1853.30 + 11436.0i 7956.11 5948.19 + 11708.5i
91.16 −20.1734 + 10.2486i 108.291i 301.934 413.497i 580.393i −1109.82 2184.60i −6232.00 −1853.30 + 11436.0i 7956.11 −5948.19 11708.5i
91.17 −19.9692 10.6410i 226.780i 285.537 + 424.985i 2286.72i −2413.17 + 4528.61i −4221.06 −1179.68 11525.0i −31746.2 −24333.0 + 45663.9i
91.18 −19.9692 10.6410i 226.780i 285.537 + 424.985i 2286.72i −2413.17 + 4528.61i 4221.06 −1179.68 11525.0i −31746.2 24333.0 45663.9i
91.19 −19.9692 + 10.6410i 226.780i 285.537 424.985i 2286.72i −2413.17 4528.61i 4221.06 −1179.68 + 11525.0i −31746.2 24333.0 + 45663.9i
91.20 −19.9692 + 10.6410i 226.780i 285.537 424.985i 2286.72i −2413.17 4528.61i −4221.06 −1179.68 + 11525.0i −31746.2 −24333.0 45663.9i
See all 100 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 91.100
Significant digits:
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Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 92.10.b.c 100
4.b odd 2 1 inner 92.10.b.c 100
23.b odd 2 1 inner 92.10.b.c 100
92.b even 2 1 inner 92.10.b.c 100
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
92.10.b.c 100 1.a even 1 1 trivial
92.10.b.c 100 4.b odd 2 1 inner
92.10.b.c 100 23.b odd 2 1 inner
92.10.b.c 100 92.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{50} + 629857 T_{3}^{48} + 184238593368 T_{3}^{46} + \cdots + 42\!\cdots\!04 \) acting on \(S_{10}^{\mathrm{new}}(92, [\chi])\). Copy content Toggle raw display