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Properties

Label 833.2.v.c
Level $833$
Weight $2$
Character orbit 833.v
Analytic conductor $6.652$
Analytic rank $0$
Dimension $64$
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] = [833,2,Mod(128,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([8, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.128");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.v (of order \(24\), degree \(8\), not 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: \(6.65153848837\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{24})\)
Twist minimal: no (minimal twist has level 119)
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 32 q^{6} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 64 q - 32 q^{6} + 24 q^{9} + 16 q^{10} + 8 q^{11} - 24 q^{12} - 16 q^{15} + 8 q^{16} - 8 q^{17} + 24 q^{18} + 24 q^{19} + 32 q^{20} - 8 q^{23} - 40 q^{24} + 8 q^{25} + 16 q^{26} + 48 q^{27} - 16 q^{31} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 16 q^{36} + 24 q^{37} - 8 q^{39} + 24 q^{40} - 16 q^{41} + 48 q^{43} + 8 q^{45} + 48 q^{46} - 208 q^{48} + 32 q^{50} - 8 q^{51} - 64 q^{52} - 16 q^{53} + 8 q^{54} + 80 q^{57} - 8 q^{58} - 8 q^{59} - 120 q^{60} + 48 q^{61} - 176 q^{62} - 48 q^{65} + 40 q^{66} + 32 q^{67} + 48 q^{68} + 32 q^{69} + 32 q^{71} - 8 q^{73} + 24 q^{74} + 24 q^{75} - 64 q^{76} + 144 q^{78} - 48 q^{79} - 56 q^{80} - 40 q^{82} + 64 q^{83} - 80 q^{85} + 8 q^{86} + 40 q^{87} - 40 q^{88} + 32 q^{90} - 112 q^{92} - 16 q^{93} + 104 q^{94} - 64 q^{95} - 112 q^{96} - 16 q^{97} - 80 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
128.1 −0.705070 − 2.63136i −0.323718 − 2.45888i −4.69487 + 2.71059i −1.49925 − 1.95386i −6.24195 + 2.58550i 0 6.59016 + 6.59016i −3.04352 + 0.815509i −4.08422 + 5.32266i
128.2 −0.590052 − 2.20210i 0.0259068 + 0.196781i −2.76905 + 1.59871i 2.37248 + 3.09188i 0.418046 − 0.173160i 0 1.93030 + 1.93030i 2.85973 − 0.766261i 5.40875 − 7.04882i
128.3 −0.462807 − 1.72722i 0.154480 + 1.17339i −1.03704 + 0.598737i −1.49976 − 1.95452i 1.95521 − 0.809875i 0 −1.01472 − 1.01472i 1.54479 − 0.413925i −2.68179 + 3.49498i
128.4 −0.208969 − 0.779883i −0.269725 − 2.04876i 1.16750 − 0.674057i 1.45971 + 1.90233i −1.54143 + 0.638482i 0 −1.91149 − 1.91149i −1.22690 + 0.328747i 1.17856 − 1.53593i
128.5 0.0353090 + 0.131775i 0.106485 + 0.808837i 1.71593 − 0.990694i −2.08640 − 2.71905i −0.102825 + 0.0425914i 0 0.384069 + 0.384069i 2.25490 − 0.604199i 0.284634 − 0.370942i
128.6 0.240930 + 0.899161i −0.143099 − 1.08695i 0.981607 − 0.566731i 0.0249560 + 0.0325233i 0.942862 − 0.390546i 0 2.06254 + 2.06254i 1.73681 − 0.465376i −0.0232311 + 0.0302753i
128.7 0.553110 + 2.06423i 0.308456 + 2.34296i −2.22308 + 1.28350i 0.412520 + 0.537607i −4.66580 + 1.93264i 0 −0.856801 − 0.856801i −2.49652 + 0.668941i −0.881578 + 1.14889i
128.8 0.619911 + 2.31354i −0.0585877 − 0.445018i −3.23613 + 1.86838i −1.43396 − 1.86877i 0.993247 − 0.411416i 0 −2.94143 − 2.94143i 2.70317 − 0.724312i 3.43455 − 4.47599i
263.1 −2.19074 − 0.587006i −0.114499 − 0.149218i 2.72270 + 1.57195i 0.148834 + 1.13051i 0.163246 + 0.394110i 0 −1.83452 − 1.83452i 0.767301 − 2.86361i 0.337559 − 2.56402i
263.2 −1.93909 − 0.519576i −2.06596 − 2.69241i 1.75804 + 1.01501i −0.166047 − 1.26125i 2.60716 + 6.29424i 0 −0.0426034 − 0.0426034i −2.20443 + 8.22706i −0.333337 + 2.53195i
263.3 −1.20384 − 0.322567i 1.30246 + 1.69740i −0.386880 − 0.223365i 0.405741 + 3.08191i −1.02042 − 2.46352i 0 2.15623 + 2.15623i −0.408302 + 1.52380i 0.505676 − 3.84099i
263.4 −0.430748 − 0.115419i −0.888577 − 1.15802i −1.55983 − 0.900567i 0.0579677 + 0.440309i 0.249096 + 0.601371i 0 1.19861 + 1.19861i 0.225025 − 0.839804i 0.0258503 − 0.196353i
263.5 0.0312663 + 0.00837777i 1.62751 + 2.12102i −1.73114 − 0.999476i −0.269658 − 2.04826i 0.0331169 + 0.0799512i 0 −0.0915300 − 0.0915300i −1.07345 + 4.00618i 0.00872863 − 0.0663005i
263.6 0.938075 + 0.251356i −1.33564 − 1.74064i −0.915246 − 0.528418i 0.364992 + 2.77239i −0.815409 − 1.96857i 0 −2.09919 − 2.09919i −0.469436 + 1.75196i −0.354468 + 2.69246i
263.7 1.23892 + 0.331968i 0.617693 + 0.804994i −0.307330 − 0.177437i −0.182482 − 1.38609i 0.498041 + 1.20238i 0 −2.13576 − 2.13576i 0.509987 − 1.90330i 0.234056 − 1.77783i
263.8 1.62429 + 0.435228i −1.39268 − 1.81497i 0.716855 + 0.413876i −0.559149 − 4.24716i −1.47219 − 3.55418i 0 −1.39388 − 1.39388i −0.578116 + 2.15756i 0.940261 − 7.14199i
410.1 −0.705070 + 2.63136i −0.323718 + 2.45888i −4.69487 − 2.71059i −1.49925 + 1.95386i −6.24195 − 2.58550i 0 6.59016 − 6.59016i −3.04352 − 0.815509i −4.08422 − 5.32266i
410.2 −0.590052 + 2.20210i 0.0259068 − 0.196781i −2.76905 − 1.59871i 2.37248 − 3.09188i 0.418046 + 0.173160i 0 1.93030 − 1.93030i 2.85973 + 0.766261i 5.40875 + 7.04882i
410.3 −0.462807 + 1.72722i 0.154480 − 1.17339i −1.03704 − 0.598737i −1.49976 + 1.95452i 1.95521 + 0.809875i 0 −1.01472 + 1.01472i 1.54479 + 0.413925i −2.68179 − 3.49498i
410.4 −0.208969 + 0.779883i −0.269725 + 2.04876i 1.16750 + 0.674057i 1.45971 − 1.90233i −1.54143 − 0.638482i 0 −1.91149 + 1.91149i −1.22690 − 0.328747i 1.17856 + 1.53593i
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 128.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner
17.d even 8 1 inner
119.q even 24 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.v.c 64
7.b odd 2 1 833.2.v.e 64
7.c even 3 1 119.2.k.a ✓ 32
7.c even 3 1 inner 833.2.v.c 64
7.d odd 6 1 833.2.l.c 32
7.d odd 6 1 833.2.v.e 64
17.d even 8 1 inner 833.2.v.c 64
119.l odd 8 1 833.2.v.e 64
119.q even 24 1 119.2.k.a ✓ 32
119.q even 24 1 inner 833.2.v.c 64
119.r odd 24 1 833.2.l.c 32
119.r odd 24 1 833.2.v.e 64
119.t odd 48 1 2023.2.a.q 16
119.t odd 48 1 2023.2.a.r 16
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
119.2.k.a ✓ 32 7.c even 3 1
119.2.k.a ✓ 32 119.q even 24 1
833.2.l.c 32 7.d odd 6 1
833.2.l.c 32 119.r odd 24 1
833.2.v.c 64 1.a even 1 1 trivial
833.2.v.c 64 7.c even 3 1 inner
833.2.v.c 64 17.d even 8 1 inner
833.2.v.c 64 119.q even 24 1 inner
833.2.v.e 64 7.b odd 2 1
833.2.v.e 64 7.d odd 6 1
833.2.v.e 64 119.l odd 8 1
833.2.v.e 64 119.r odd 24 1
2023.2.a.q 16 119.t odd 48 1
2023.2.a.r 16 119.t odd 48 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(833, [\chi])\):

\( T_{2}^{64} - 102 T_{2}^{60} + 8 T_{2}^{59} - 88 T_{2}^{57} + 6809 T_{2}^{56} + 624 T_{2}^{55} + 32 T_{2}^{54} + \cdots + 1 \) Copy content Toggle raw display
\( T_{3}^{64} - 12 T_{3}^{62} - 48 T_{3}^{61} + 72 T_{3}^{60} + 424 T_{3}^{59} + 32 T_{3}^{58} + \cdots + 923521 \) Copy content Toggle raw display