Properties

Label 483.2.bc.a
Level $483$
Weight $2$
Character orbit 483.bc
Analytic conductor $3.857$
Analytic rank $0$
Dimension $1200$
CM no
Inner twists $8$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.bc (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(1200\)
Relative dimension: \(60\) over \(\Q(\zeta_{66})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1200q - 9q^{3} - 74q^{4} - 20q^{6} - 44q^{7} - 13q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 1200q - 9q^{3} - 74q^{4} - 20q^{6} - 44q^{7} - 13q^{9} - 22q^{10} - 25q^{12} - 72q^{13} - 44q^{15} + 38q^{16} - 45q^{18} - 22q^{19} + 44q^{21} + 2q^{24} + 18q^{25} - 90q^{27} - 44q^{28} - 55q^{30} - 18q^{31} - 11q^{33} - 88q^{34} - 108q^{36} - 66q^{37} + q^{39} - 22q^{40} - 22q^{42} - 2q^{46} - 228q^{48} - 128q^{49} - 11q^{51} - 166q^{52} + 35q^{54} - 160q^{55} - 44q^{57} - 126q^{58} - 11q^{60} + 66q^{61} + 33q^{63} + 40q^{64} + 22q^{66} - 22q^{67} - 24q^{69} + 68q^{70} - 149q^{72} - 42q^{73} + 123q^{75} - 88q^{76} - 108q^{78} - 66q^{79} - 81q^{81} - 14q^{82} + 44q^{84} - 200q^{85} + 75q^{87} + 66q^{88} + 16q^{93} - 146q^{94} + 5q^{96} - 88q^{97} - 308q^{99} + O(q^{100}) \)

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.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1 −1.22080 + 2.36802i 1.28284 1.16376i −2.95705 4.15260i −2.00169 1.90861i 1.18972 + 4.45849i 1.48870 + 2.18719i 8.16926 1.17456i 0.291334 2.98582i 6.96327 2.41001i
11.2 −1.21990 + 2.36628i 0.543753 + 1.64449i −2.95102 4.14413i 1.29182 + 1.23174i −4.55465 0.719442i −2.63893 0.189827i 8.13588 1.16976i −2.40867 + 1.78839i −4.49055 + 1.55419i
11.3 −1.20831 + 2.34379i −1.45411 + 0.941049i −2.87322 4.03487i 0.0368505 + 0.0351369i −0.448612 4.54519i 0.406340 + 2.61436i 7.70844 1.10831i 1.22885 2.73677i −0.126880 + 0.0439136i
11.4 −1.14211 + 2.21537i 1.18000 + 1.26791i −2.44337 3.43123i −2.09226 1.99497i −4.15658 + 1.16606i 2.18985 1.48478i 5.45789 0.784726i −0.215184 + 2.99227i 6.80917 2.35668i
11.5 −1.13087 + 2.19357i −1.61171 + 0.634352i −2.37279 3.33212i −2.21831 2.11515i 0.431125 4.25276i 0.0462933 2.64535i 5.10697 0.734272i 2.19519 2.04478i 7.14835 2.47407i
11.6 −1.11786 + 2.16834i 1.70544 0.302424i −2.29198 3.21863i 1.96583 + 1.87442i −1.25068 + 4.03605i 1.12495 2.39468i 4.71179 0.677453i 2.81708 1.03153i −6.26189 + 2.16726i
11.7 −1.07488 + 2.08498i 0.382326 1.68933i −2.03164 2.85304i 2.47963 + 2.36432i 3.11125 + 2.61296i −0.426197 + 2.61120i 3.48857 0.501581i −2.70765 1.29175i −7.59486 + 2.62861i
11.8 −1.02175 + 1.98192i −1.59600 0.672881i −1.72392 2.42090i 1.12079 + 1.06868i 2.96432 2.47564i −2.59123 + 0.534343i 2.14526 0.308441i 2.09446 + 2.14784i −3.26320 + 1.12941i
11.9 −0.970052 + 1.88164i −0.673848 + 1.59560i −1.43945 2.02142i 2.06335 + 1.96740i −2.34867 2.81575i 2.64569 0.0181926i 1.00908 0.145084i −2.09186 2.15038i −5.70349 + 1.97400i
11.10 −0.918620 + 1.78187i −1.09876 1.33893i −1.17110 1.64458i −2.94599 2.80900i 3.39514 0.727879i −1.97640 + 1.75893i 0.0375805 0.00540327i −0.585467 + 2.94232i 7.71152 2.66898i
11.11 −0.877897 + 1.70288i −0.523928 1.65091i −0.968993 1.36076i −0.190109 0.181269i 3.27126 + 0.557140i 2.56678 0.641583i −0.624824 + 0.0898362i −2.45100 + 1.72991i 0.475576 0.164598i
11.12 −0.839802 + 1.62899i 0.824775 1.52307i −0.788222 1.10690i −0.179075 0.170747i 1.78842 + 2.62263i −1.48519 2.18957i −1.16305 + 0.167222i −1.63949 2.51238i 0.428532 0.148317i
11.13 −0.839508 + 1.62842i 1.58694 + 0.693981i −0.786858 1.10499i −1.28009 1.22056i −2.46234 + 2.00161i −1.82028 + 1.92005i −1.16691 + 0.167776i 2.03678 + 2.20262i 3.06224 1.05985i
11.14 −0.823961 + 1.59826i 1.52148 + 0.827710i −0.715414 1.00466i 1.91038 + 1.82155i −2.57654 + 1.74972i 1.62874 + 2.08499i −1.36452 + 0.196188i 1.62979 + 2.51868i −4.48539 + 1.55241i
11.15 −0.745161 + 1.44541i −1.73201 0.0112995i −0.373834 0.524976i 1.43978 + 1.37282i 1.30696 2.49505i 0.470528 2.60358i −2.18189 + 0.313709i 2.99974 + 0.0391417i −3.05716 + 1.05809i
11.16 −0.742085 + 1.43944i −0.310505 + 1.70399i −0.361196 0.507229i −1.42767 1.36128i −2.22238 1.71146i −2.18159 1.49689i −2.20781 + 0.317435i −2.80717 1.05820i 3.01893 1.04486i
11.17 −0.583726 + 1.13227i 1.30843 1.13490i 0.218812 + 0.307278i −1.12328 1.07105i 0.521253 + 2.14397i 2.07224 + 1.64494i −2.99748 + 0.430973i 0.423986 2.96989i 1.86841 0.646663i
11.18 −0.571670 + 1.10889i −1.29954 + 1.14507i 0.257294 + 0.361318i −1.77881 1.69609i −0.526840 2.09565i 0.0113481 + 2.64573i −3.01749 + 0.433850i 0.377631 2.97614i 2.89767 1.00289i
11.19 −0.528482 + 1.02511i −1.73132 0.0502508i 0.388554 + 0.545647i −0.207815 0.198151i 0.966484 1.74824i 2.41072 + 1.09014i −3.04785 + 0.438215i 2.99495 + 0.174001i 0.312954 0.108314i
11.20 −0.522802 + 1.01409i −1.07403 + 1.35885i 0.405048 + 0.568811i 2.77635 + 2.64725i −0.816498 1.79957i −2.48243 + 0.915168i −3.04721 + 0.438123i −0.692939 2.91888i −4.13604 + 1.43150i
See next 80 embeddings (of 1200 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 452.60
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.c even 3 1 inner
21.h odd 6 1 inner
23.d odd 22 1 inner
69.g even 22 1 inner
161.p odd 66 1 inner
483.bc even 66 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.2.bc.a 1200
3.b odd 2 1 inner 483.2.bc.a 1200
7.c even 3 1 inner 483.2.bc.a 1200
21.h odd 6 1 inner 483.2.bc.a 1200
23.d odd 22 1 inner 483.2.bc.a 1200
69.g even 22 1 inner 483.2.bc.a 1200
161.p odd 66 1 inner 483.2.bc.a 1200
483.bc even 66 1 inner 483.2.bc.a 1200
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.bc.a 1200 1.a even 1 1 trivial
483.2.bc.a 1200 3.b odd 2 1 inner
483.2.bc.a 1200 7.c even 3 1 inner
483.2.bc.a 1200 21.h odd 6 1 inner
483.2.bc.a 1200 23.d odd 22 1 inner
483.2.bc.a 1200 69.g even 22 1 inner
483.2.bc.a 1200 161.p odd 66 1 inner
483.2.bc.a 1200 483.bc even 66 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(483, [\chi])\).