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Properties

Label 833.2.bl.a
Level $833$
Weight $2$
Character orbit 833.bl
Analytic conductor $6.652$
Analytic rank $0$
Dimension $3936$
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(2,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(168))
 
chi = DirichletCharacter(H, H._module([104, 147]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.bl (of order \(168\), degree \(48\), 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: \(3936\)
Relative dimension: \(82\) over \(\Q(\zeta_{168})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{168}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3936 q - 52 q^{2} - 52 q^{3} - 56 q^{5} - 40 q^{6} - 48 q^{7} - 24 q^{8} - 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 3936 q - 52 q^{2} - 52 q^{3} - 56 q^{5} - 40 q^{6} - 48 q^{7} - 24 q^{8} - 52 q^{9} - 52 q^{10} - 20 q^{11} - 28 q^{12} - 88 q^{14} - 64 q^{15} - 408 q^{16} - 60 q^{17} - 32 q^{18} - 24 q^{19} - 8 q^{20} - 8 q^{22} - 148 q^{23} - 28 q^{24} - 48 q^{25} - 92 q^{26} + 8 q^{27} + 80 q^{28} - 40 q^{29} - 24 q^{31} - 104 q^{32} - 152 q^{33} - 40 q^{34} - 112 q^{35} + 32 q^{36} - 36 q^{37} - 64 q^{39} + 140 q^{40} + 16 q^{41} + 196 q^{42} - 40 q^{43} + 108 q^{44} - 64 q^{45} - 52 q^{46} - 168 q^{48} - 212 q^{49} - 160 q^{50} - 92 q^{51} - 88 q^{52} - 52 q^{53} + 4 q^{54} - 28 q^{56} - 40 q^{57} + 156 q^{58} + 52 q^{59} - 156 q^{60} - 32 q^{61} - 144 q^{62} - 36 q^{63} - 72 q^{65} - 68 q^{66} - 56 q^{67} + 32 q^{68} + 32 q^{69} - 132 q^{70} - 216 q^{71} - 32 q^{73} - 52 q^{74} + 388 q^{75} - 160 q^{76} - 56 q^{77} + 72 q^{78} - 40 q^{79} + 16 q^{80} - 360 q^{82} - 52 q^{83} - 152 q^{84} - 48 q^{85} - 136 q^{86} - 124 q^{87} + 504 q^{88} - 120 q^{90} - 120 q^{91} - 88 q^{92} - 276 q^{93} + 236 q^{94} + 360 q^{95} - 380 q^{96} - 192 q^{97} - 544 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −1.29381 − 2.44800i −0.00548377 − 0.293216i −3.19214 + 4.68201i −1.67310 − 2.77666i −0.710699 + 0.392789i −2.25416 + 1.38519i 10.0887 + 1.13672i 2.91196 − 0.108958i −4.63260 + 7.68821i
2.2 −1.28880 − 2.43852i 0.0516840 + 2.76353i −3.15875 + 4.63303i 0.290875 + 0.482734i 6.67232 − 3.68766i 2.19827 − 1.47228i 9.88712 + 1.11401i −4.63654 + 0.173487i 0.802277 − 1.33145i
2.3 −1.21927 − 2.30698i 0.00453835 + 0.242665i −2.70888 + 3.97320i 1.92733 + 3.19858i 0.554289 − 0.306345i −1.37035 − 2.26321i 7.28304 + 0.820601i 2.93904 − 0.109971i 5.02911 − 8.34627i
2.4 −1.20942 − 2.28833i −0.0275471 − 1.47294i −2.64713 + 3.88262i 0.0276342 + 0.0458614i −3.33726 + 1.84444i 2.16245 + 1.52440i 6.94222 + 0.782201i 0.829108 − 0.0310230i 0.0715249 − 0.118702i
2.5 −1.18854 − 2.24883i −0.0504252 − 2.69623i −2.51797 + 3.69319i 0.173885 + 0.288577i −6.00343 + 3.31798i −2.63642 − 0.222024i 6.24288 + 0.703404i −4.26919 + 0.159742i 0.442292 − 0.734024i
2.6 −1.18721 − 2.24632i 0.0455765 + 2.43697i −2.50982 + 3.68123i 0.320193 + 0.531389i 5.42009 − 2.99558i −1.79641 + 1.94240i 6.19934 + 0.698498i −2.93884 + 0.109963i 0.813530 − 1.35013i
2.7 −1.16880 − 2.21148i −0.0544346 − 2.91061i −2.39791 + 3.51709i 1.40263 + 2.32779i −6.37313 + 3.52230i 2.33407 − 1.24583i 5.60941 + 0.632029i −5.47076 + 0.204702i 3.50846 − 5.82260i
2.8 −1.14872 − 2.17348i 0.00950488 + 0.508225i −2.27781 + 3.34093i −1.13451 − 1.88282i 1.09370 − 0.604464i 2.53192 + 0.767720i 4.99218 + 0.562484i 2.73970 − 0.102512i −2.78904 + 4.62865i
2.9 −1.07775 − 2.03921i 0.0334431 + 1.78820i −1.87018 + 2.74304i 1.19245 + 1.97898i 3.61046 − 1.99543i −0.295065 + 2.62925i 3.02524 + 0.340862i −0.198621 + 0.00743189i 2.75039 − 4.56451i
2.10 −1.07547 − 2.03489i 0.00679539 + 0.363348i −1.85750 + 2.72445i −0.459596 − 0.762741i 0.732066 − 0.404598i 0.536901 − 2.59070i 2.96737 + 0.334342i 2.86593 − 0.107235i −1.05781 + 1.75553i
2.11 −1.05997 − 2.00557i 0.0423999 + 2.26711i −1.77212 + 2.59922i −2.26230 − 3.75449i 4.50191 − 2.48812i −0.755182 − 2.53569i 2.58294 + 0.291028i −2.14010 + 0.0800771i −5.13190 + 8.51685i
2.12 −1.03910 − 1.96608i −0.0495380 − 2.64879i −1.65908 + 2.43343i −1.98476 − 3.29390i −5.15625 + 2.84976i 1.77933 − 1.95806i 2.08867 + 0.235336i −4.01574 + 0.150258i −4.41368 + 7.32489i
2.13 −0.969389 − 1.83417i 0.0177845 + 0.950937i −1.29784 + 1.90358i 0.178302 + 0.295908i 1.72694 − 0.954448i −2.63124 − 0.276714i 0.626527 + 0.0705927i 2.09394 − 0.0783496i 0.369902 − 0.613886i
2.14 −0.927490 − 1.75490i 0.0227529 + 1.21659i −1.09279 + 1.60282i 1.86921 + 3.10212i 2.11389 − 1.16831i 2.62836 + 0.302821i −0.118537 − 0.0133559i 1.51832 − 0.0568116i 3.71023 − 6.15746i
2.15 −0.920659 − 1.74197i −0.0368197 − 1.96875i −1.06021 + 1.55504i −0.454599 − 0.754447i −3.39560 + 1.87668i −1.82538 − 1.91519i −0.230884 − 0.0260144i −0.876700 + 0.0328038i −0.895695 + 1.48649i
2.16 −0.915515 − 1.73224i −0.0261882 − 1.40028i −1.03585 + 1.51931i 0.303922 + 0.504386i −2.40164 + 1.32734i 0.494399 + 2.59915i −0.313807 − 0.0353576i 1.03781 − 0.0388320i 0.595471 − 0.988238i
2.17 −0.915320 − 1.73187i −0.0450864 − 2.41076i −1.03492 + 1.51795i −1.91137 − 3.17210i −4.13386 + 2.28470i −0.478411 + 2.60214i −0.316925 − 0.0357089i −2.81184 + 0.105212i −3.74414 + 6.21374i
2.18 −0.857332 − 1.62215i 0.0550248 + 2.94217i −0.769718 + 1.12897i −0.142485 − 0.236467i 4.72546 − 2.61167i −2.30274 − 1.30283i −1.15521 − 0.130161i −5.65541 + 0.211610i −0.261429 + 0.433864i
2.19 −0.856882 − 1.62130i −0.0102250 − 0.546729i −0.767728 + 1.12605i 1.33377 + 2.21350i −0.877650 + 0.485060i 2.40268 − 1.10775i −1.16104 − 0.130818i 2.69909 − 0.100993i 2.44587 − 4.05915i
2.20 −0.788333 − 1.49160i 0.0621420 + 3.32272i −0.476757 + 0.699275i 0.428421 + 0.711004i 4.90718 − 2.71210i 2.62715 + 0.313219i −1.93412 − 0.217923i −8.03871 + 0.300787i 0.722793 − 1.19954i
See next 80 embeddings (of 3936 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.82
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.d even 8 1 inner
49.g even 21 1 inner
833.bl even 168 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.bl.a ✓ 3936
17.d even 8 1 inner 833.2.bl.a ✓ 3936
49.g even 21 1 inner 833.2.bl.a ✓ 3936
833.bl even 168 1 inner 833.2.bl.a ✓ 3936
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.bl.a ✓ 3936 1.a even 1 1 trivial
833.2.bl.a ✓ 3936 17.d even 8 1 inner
833.2.bl.a ✓ 3936 49.g even 21 1 inner
833.2.bl.a ✓ 3936 833.bl even 168 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(833, [\chi])\).