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Properties

Label 92.3.c.a
Level $92$
Weight $3$
Character orbit 92.c
Analytic conductor $2.507$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [92,3,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, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("92.47");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
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: \(2.50681843211\)
Analytic rank: \(0\)
Dimension: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 4 q^{5} - 3 q^{6} - 3 q^{8} - 58 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q - 4 q^{5} - 3 q^{6} - 3 q^{8} - 58 q^{9} + 10 q^{10} + q^{12} - 4 q^{13} - 8 q^{14} + 16 q^{16} - 4 q^{17} - 43 q^{18} - 44 q^{20} + 48 q^{21} + 44 q^{22} - 20 q^{24} + 66 q^{25} + 77 q^{26} + 114 q^{28} - 20 q^{29} - 74 q^{30} + 40 q^{32} + 32 q^{33} + 42 q^{34} - 45 q^{36} - 100 q^{37} - 124 q^{38} - 130 q^{40} - 20 q^{41} + 120 q^{42} - 10 q^{44} + 60 q^{45} - 5 q^{48} - 26 q^{49} - 160 q^{50} + 71 q^{52} + 12 q^{53} + 199 q^{54} + 34 q^{56} - 153 q^{58} + 60 q^{60} + 60 q^{61} - 23 q^{62} + 147 q^{64} - 88 q^{65} + 30 q^{66} - 380 q^{68} + 204 q^{70} - 201 q^{72} - 4 q^{73} - 282 q^{74} + 128 q^{76} - 80 q^{77} - 65 q^{78} + 46 q^{80} - 154 q^{81} + 73 q^{82} + 590 q^{84} + 104 q^{85} + 426 q^{86} - 324 q^{88} + 332 q^{89} + 4 q^{90} - 192 q^{93} - 7 q^{94} + 507 q^{96} + 44 q^{97} + 148 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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 −1.99708 − 0.108004i − 3.85792i 3.97667 + 0.431387i 4.86708 −0.416672 + 7.70457i − 0.333672i −7.89514 − 1.29101i −5.88352 −9.71996 − 0.525667i
47.2 −1.99708 + 0.108004i 3.85792i 3.97667 − 0.431387i 4.86708 −0.416672 − 7.70457i 0.333672i −7.89514 + 1.29101i −5.88352 −9.71996 + 0.525667i
47.3 −1.82516 − 0.817799i 2.65354i 2.66241 + 2.98523i −8.55981 2.17007 − 4.84314i − 9.76977i −2.41800 − 7.62583i 1.95871 15.6230 + 7.00021i
47.4 −1.82516 + 0.817799i − 2.65354i 2.66241 − 2.98523i −8.55981 2.17007 + 4.84314i 9.76977i −2.41800 + 7.62583i 1.95871 15.6230 − 7.00021i
47.5 −1.51168 − 1.30951i 0.202799i 0.570366 + 3.95913i 0.912126 0.265568 − 0.306568i 9.62842i 4.32231 − 6.73184i 8.95887 −1.37884 − 1.19444i
47.6 −1.51168 + 1.30951i − 0.202799i 0.570366 − 3.95913i 0.912126 0.265568 + 0.306568i − 9.62842i 4.32231 + 6.73184i 8.95887 −1.37884 + 1.19444i
47.7 −1.11001 − 1.66369i − 4.84820i −1.53574 + 3.69344i −3.26050 −8.06591 + 5.38157i − 6.48063i 7.84944 − 1.54476i −14.5051 3.61920 + 5.42447i
47.8 −1.11001 + 1.66369i 4.84820i −1.53574 − 3.69344i −3.26050 −8.06591 − 5.38157i 6.48063i 7.84944 + 1.54476i −14.5051 3.61920 − 5.42447i
47.9 −0.477277 − 1.94222i 1.49808i −3.54441 + 1.85395i 6.24241 2.90960 − 0.715000i − 9.66247i 5.29244 + 5.99917i 6.75575 −2.97936 − 12.1241i
47.10 −0.477277 + 1.94222i − 1.49808i −3.54441 − 1.85395i 6.24241 2.90960 + 0.715000i 9.66247i 5.29244 − 5.99917i 6.75575 −2.97936 + 12.1241i
47.11 −0.0385346 − 1.99963i 4.25333i −3.99703 + 0.154110i −5.13542 8.50508 − 0.163900i 4.91814i 0.462187 + 7.98664i −9.09082 0.197892 + 10.2689i
47.12 −0.0385346 + 1.99963i − 4.25333i −3.99703 − 0.154110i −5.13542 8.50508 + 0.163900i − 4.91814i 0.462187 − 7.98664i −9.09082 0.197892 − 10.2689i
47.13 0.706844 − 1.87093i − 4.16432i −3.00074 − 2.64491i 7.90969 −7.79114 − 2.94352i 4.74734i −7.06949 + 3.74464i −8.34154 5.59092 − 14.7985i
47.14 0.706844 + 1.87093i 4.16432i −3.00074 + 2.64491i 7.90969 −7.79114 + 2.94352i − 4.74734i −7.06949 − 3.74464i −8.34154 5.59092 + 14.7985i
47.15 0.951506 − 1.75916i − 1.56531i −2.18927 − 3.34770i −6.25225 −2.75363 − 1.48940i − 3.62931i −7.97224 + 0.665927i 6.54979 −5.94905 + 10.9987i
47.16 0.951506 + 1.75916i 1.56531i −2.18927 + 3.34770i −6.25225 −2.75363 + 1.48940i 3.62931i −7.97224 − 0.665927i 6.54979 −5.94905 − 10.9987i
47.17 1.44877 − 1.37879i 3.59730i 0.197898 − 3.99510i 4.81203 4.95991 + 5.21168i 7.29038i −5.22168 − 6.06086i −3.94058 6.97155 − 6.63476i
47.18 1.44877 + 1.37879i − 3.59730i 0.197898 + 3.99510i 4.81203 4.95991 − 5.21168i − 7.29038i −5.22168 + 6.06086i −3.94058 6.97155 + 6.63476i
47.19 1.86082 − 0.733050i − 0.414828i 2.92528 − 2.72814i −0.506901 −0.304089 − 0.771919i − 4.35621i 3.44354 − 7.22094i 8.82792 −0.943249 + 0.371583i
47.20 1.86082 + 0.733050i 0.414828i 2.92528 + 2.72814i −0.506901 −0.304089 + 0.771919i 4.35621i 3.44354 + 7.22094i 8.82792 −0.943249 − 0.371583i
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 47.22
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 92.3.c.a ✓ 22
4.b odd 2 1 inner 92.3.c.a ✓ 22
8.b even 2 1 1472.3.d.e 22
8.d odd 2 1 1472.3.d.e 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
92.3.c.a ✓ 22 1.a even 1 1 trivial
92.3.c.a ✓ 22 4.b odd 2 1 inner
1472.3.d.e 22 8.b even 2 1
1472.3.d.e 22 8.d odd 2 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(92, [\chi])\).