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Properties

Label 920.2.y.a
Level $920$
Weight $2$
Character orbit 920.y
Analytic conductor $7.346$
Analytic rank $0$
Dimension $50$
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] = [920,2,Mod(41,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.y (of order \(11\), degree \(10\), 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: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 50 q + q^{3} + 5 q^{5} + 9 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 50 q + q^{3} + 5 q^{5} + 9 q^{7} - 6 q^{9} + q^{11} - 8 q^{13} - q^{15} - 26 q^{17} + 12 q^{19} - 4 q^{21} - q^{23} - 5 q^{25} - 35 q^{27} + 38 q^{29} - 9 q^{31} - 31 q^{33} + 2 q^{35} - 31 q^{37} + 3 q^{39} + 39 q^{41} + 8 q^{43} - 16 q^{45} - 32 q^{47} + 44 q^{49} + 52 q^{51} - 8 q^{53} + 10 q^{55} - 18 q^{57} - 32 q^{59} - 39 q^{61} - 74 q^{63} + 19 q^{65} - 26 q^{67} - 78 q^{69} - 18 q^{71} - 18 q^{73} + q^{75} + 98 q^{77} - 23 q^{79} - 21 q^{81} - 57 q^{83} + 4 q^{85} - 6 q^{87} - 85 q^{89} - 14 q^{91} - 98 q^{93} + 21 q^{95} - 33 q^{97} + 19 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
41.1 0 −1.67176 + 1.92931i 0 0.142315 − 0.989821i 0 0.701198 + 1.53541i 0 −0.500523 − 3.48121i 0
41.2 0 −1.31340 + 1.51574i 0 0.142315 − 0.989821i 0 −0.400657 − 0.877315i 0 −0.145513 − 1.01207i 0
41.3 0 0.369496 − 0.426421i 0 0.142315 − 0.989821i 0 0.800903 + 1.75373i 0 0.381637 + 2.65434i 0
41.4 0 1.10382 − 1.27388i 0 0.142315 − 0.989821i 0 0.431379 + 0.944588i 0 0.0226026 + 0.157205i 0
41.5 0 2.16670 − 2.50050i 0 0.142315 − 0.989821i 0 −1.18768 − 2.60066i 0 −1.13099 − 7.86620i 0
81.1 0 −0.282423 + 1.96429i 0 0.959493 − 0.281733i 0 −1.18218 − 1.36431i 0 −0.900213 − 0.264326i 0
81.2 0 −0.203836 + 1.41771i 0 0.959493 − 0.281733i 0 2.32183 + 2.67953i 0 0.910126 + 0.267237i 0
81.3 0 0.00837462 − 0.0582467i 0 0.959493 − 0.281733i 0 −1.65927 − 1.91490i 0 2.87516 + 0.844222i 0
81.4 0 0.203480 − 1.41524i 0 0.959493 − 0.281733i 0 −1.26516 − 1.46007i 0 0.916986 + 0.269251i 0
81.5 0 0.416719 − 2.89834i 0 0.959493 − 0.281733i 0 2.64247 + 3.04957i 0 −5.34826 − 1.57039i 0
121.1 0 −2.12338 − 0.623480i 0 −0.841254 + 0.540641i 0 0.0555147 − 0.386113i 0 1.59624 + 1.02584i 0
121.2 0 −1.46823 − 0.431112i 0 −0.841254 + 0.540641i 0 0.463590 − 3.22434i 0 −0.553909 − 0.355976i 0
121.3 0 0.573111 + 0.168280i 0 −0.841254 + 0.540641i 0 −0.624523 + 4.34366i 0 −2.22362 − 1.42904i 0
121.4 0 1.16946 + 0.343384i 0 −0.841254 + 0.540641i 0 0.227903 − 1.58510i 0 −1.27404 − 0.818778i 0
121.5 0 2.80854 + 0.824660i 0 −0.841254 + 0.540641i 0 −0.0819769 + 0.570162i 0 4.68404 + 3.01025i 0
361.1 0 −1.76017 + 1.13119i 0 −0.415415 − 0.909632i 0 −2.92925 + 0.860106i 0 0.572354 − 1.25328i 0
361.2 0 −1.26851 + 0.815223i 0 −0.415415 − 0.909632i 0 2.02904 − 0.595779i 0 −0.301712 + 0.660657i 0
361.3 0 0.348206 − 0.223778i 0 −0.415415 − 0.909632i 0 −2.39931 + 0.704501i 0 −1.17507 + 2.57305i 0
361.4 0 0.846736 − 0.544164i 0 −0.415415 − 0.909632i 0 4.62632 − 1.35841i 0 −0.825398 + 1.80737i 0
361.5 0 0.992485 − 0.637832i 0 −0.415415 − 0.909632i 0 0.514454 − 0.151057i 0 −0.668047 + 1.46282i 0
See all 50 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 41.5
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 920.2.y.a ✓ 50
23.c even 11 1 inner 920.2.y.a ✓ 50
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
920.2.y.a ✓ 50 1.a even 1 1 trivial
920.2.y.a ✓ 50 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{50} - T_{3}^{49} + 11 T_{3}^{48} - T_{3}^{47} + 92 T_{3}^{46} - 38 T_{3}^{45} + 521 T_{3}^{44} + \cdots + 326041 \) acting on \(S_{2}^{\mathrm{new}}(920, [\chi])\). Copy content Toggle raw display