Properties

Label 483.2.m.a
Level $483$
Weight $2$
Character orbit 483.m
Analytic conductor $3.857$
Analytic rank $0$
Dimension $120$
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.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(60\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 120q - 2q^{3} + 52q^{4} - 24q^{6} + 2q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 120q - 2q^{3} + 52q^{4} - 24q^{6} + 2q^{9} + 14q^{12} - 16q^{13} - 60q^{16} - 10q^{18} - 24q^{24} - 40q^{25} - 20q^{27} - 4q^{31} + 64q^{36} - 12q^{39} - 20q^{46} + 140q^{48} - 48q^{49} - 76q^{52} - 2q^{54} + 72q^{55} - 28q^{58} - 128q^{64} - 20q^{69} - 68q^{70} + 6q^{72} + 20q^{73} + 20q^{75} - 156q^{78} - 62q^{81} + 80q^{82} + 112q^{85} + 46q^{87} - 38q^{93} + 36q^{94} + 72q^{96} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
137.1 −2.35341 + 1.35874i 1.22585 + 1.22364i 2.69235 4.66329i −1.88300 3.26145i −4.54753 1.21410i −0.393331 2.61635i 9.19786i 0.00542953 + 3.00000i 8.86291 + 5.11701i
137.2 −2.35341 + 1.35874i 1.22585 + 1.22364i 2.69235 4.66329i 1.88300 + 3.26145i −4.54753 1.21410i 0.393331 + 2.61635i 9.19786i 0.00542953 + 3.00000i −8.86291 5.11701i
137.3 −2.20025 + 1.27031i −1.66604 0.473602i 2.22739 3.85796i −0.823724 1.42673i 4.26733 1.07436i −2.24449 + 1.40082i 6.23669i 2.55140 + 1.57808i 3.62479 + 2.09277i
137.4 −2.20025 + 1.27031i −1.66604 0.473602i 2.22739 3.85796i 0.823724 + 1.42673i 4.26733 1.07436i 2.24449 1.40082i 6.23669i 2.55140 + 1.57808i −3.62479 2.09277i
137.5 −2.14419 + 1.23795i −0.991594 + 1.42012i 2.06503 3.57673i −0.969003 1.67836i 0.368129 4.27255i 0.562535 + 2.58526i 5.27380i −1.03348 2.81637i 4.15545 + 2.39915i
137.6 −2.14419 + 1.23795i −0.991594 + 1.42012i 2.06503 3.57673i 0.969003 + 1.67836i 0.368129 4.27255i −0.562535 2.58526i 5.27380i −1.03348 2.81637i −4.15545 2.39915i
137.7 −2.05926 + 1.18892i 1.51759 0.834823i 1.82704 3.16453i −0.178457 0.309097i −2.13257 + 3.52340i 2.62376 + 0.340385i 3.93312i 1.60614 2.53383i 0.734981 + 0.424342i
137.8 −2.05926 + 1.18892i 1.51759 0.834823i 1.82704 3.16453i 0.178457 + 0.309097i −2.13257 + 3.52340i −2.62376 0.340385i 3.93312i 1.60614 2.53383i −0.734981 0.424342i
137.9 −1.78161 + 1.02861i 0.0211372 1.73192i 1.11608 1.93311i −1.27213 2.20340i 1.74382 + 3.10735i −0.668238 2.55997i 0.477615i −2.99911 0.0732160i 4.53288 + 2.61706i
137.10 −1.78161 + 1.02861i 0.0211372 1.73192i 1.11608 1.93311i 1.27213 + 2.20340i 1.74382 + 3.10735i 0.668238 + 2.55997i 0.477615i −2.99911 0.0732160i −4.53288 2.61706i
137.11 −1.55658 + 0.898694i 0.279659 + 1.70932i 0.615303 1.06574i −0.620314 1.07442i −1.97147 2.40938i −2.49407 + 0.882968i 1.38290i −2.84358 + 0.956058i 1.93114 + 1.11495i
137.12 −1.55658 + 0.898694i 0.279659 + 1.70932i 0.615303 1.06574i 0.620314 + 1.07442i −1.97147 2.40938i 2.49407 0.882968i 1.38290i −2.84358 + 0.956058i −1.93114 1.11495i
137.13 −1.44748 + 0.835704i 1.59432 + 0.676852i 0.396802 0.687281i −1.25144 2.16756i −2.87340 + 0.352653i 2.40151 + 1.11029i 2.01638i 2.08374 + 2.15824i 3.62287 + 2.09167i
137.14 −1.44748 + 0.835704i 1.59432 + 0.676852i 0.396802 0.687281i 1.25144 + 2.16756i −2.87340 + 0.352653i −2.40151 1.11029i 2.01638i 2.08374 + 2.15824i −3.62287 2.09167i
137.15 −1.28014 + 0.739089i −1.73064 + 0.0699156i 0.0925045 0.160222i −0.974027 1.68706i 2.16379 1.36860i −2.08240 1.63205i 2.68288i 2.99022 0.241997i 2.49378 + 1.43978i
137.16 −1.28014 + 0.739089i −1.73064 + 0.0699156i 0.0925045 0.160222i 0.974027 + 1.68706i 2.16379 1.36860i 2.08240 + 1.63205i 2.68288i 2.99022 0.241997i −2.49378 1.43978i
137.17 −1.19221 + 0.688323i 1.08950 1.34647i −0.0524225 + 0.0907985i −2.03563 3.52582i −0.372109 + 2.35521i −1.00571 + 2.44715i 2.89763i −0.625968 2.93397i 4.85381 + 2.80235i
137.18 −1.19221 + 0.688323i 1.08950 1.34647i −0.0524225 + 0.0907985i 2.03563 + 3.52582i −0.372109 + 2.35521i 1.00571 2.44715i 2.89763i −0.625968 2.93397i −4.85381 2.80235i
137.19 −0.935072 + 0.539864i −0.991443 1.42023i −0.417093 + 0.722427i −0.281343 0.487300i 1.69380 + 0.792769i −1.64560 + 2.07172i 3.06015i −1.03408 + 2.81615i 0.526152 + 0.303774i
137.20 −0.935072 + 0.539864i −0.991443 1.42023i −0.417093 + 0.722427i 0.281343 + 0.487300i 1.69380 + 0.792769i 1.64560 2.07172i 3.06015i −1.03408 + 2.81615i −0.526152 0.303774i
See next 80 embeddings (of 120 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 275.60
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.b odd 2 1 inner
69.c even 2 1 inner
161.f odd 6 1 inner
483.m even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.2.m.a 120
3.b odd 2 1 inner 483.2.m.a 120
7.c even 3 1 inner 483.2.m.a 120
21.h odd 6 1 inner 483.2.m.a 120
23.b odd 2 1 inner 483.2.m.a 120
69.c even 2 1 inner 483.2.m.a 120
161.f odd 6 1 inner 483.2.m.a 120
483.m even 6 1 inner 483.2.m.a 120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.m.a 120 1.a even 1 1 trivial
483.2.m.a 120 3.b odd 2 1 inner
483.2.m.a 120 7.c even 3 1 inner
483.2.m.a 120 21.h odd 6 1 inner
483.2.m.a 120 23.b odd 2 1 inner
483.2.m.a 120 69.c even 2 1 inner
483.2.m.a 120 161.f odd 6 1 inner
483.2.m.a 120 483.m even 6 1 inner

Hecke kernels

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