Properties

Label 483.2.q.e
Level $483$
Weight $2$
Character orbit 483.q
Analytic conductor $3.857$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 60q - q^{2} + 6q^{3} - 3q^{4} + 5q^{5} + q^{6} + 6q^{7} + 13q^{8} - 6q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 60q - q^{2} + 6q^{3} - 3q^{4} + 5q^{5} + q^{6} + 6q^{7} + 13q^{8} - 6q^{9} - 4q^{10} - q^{11} + 3q^{12} + 22q^{13} + q^{14} + 6q^{15} - 5q^{16} + 9q^{17} - q^{18} - 34q^{19} + 67q^{20} - 6q^{21} - 28q^{22} - 13q^{23} + 42q^{24} - 15q^{25} - 4q^{26} + 6q^{27} + 14q^{28} - 23q^{29} + 4q^{30} + 27q^{31} + 37q^{32} + q^{33} + 3q^{34} + 6q^{35} - 3q^{36} - 82q^{37} + 2q^{38} - 22q^{39} + 57q^{40} - 22q^{41} - q^{42} + 25q^{43} - 41q^{44} + 16q^{45} - 47q^{46} - 90q^{47} - 28q^{48} - 6q^{49} + 55q^{50} - 9q^{51} - 92q^{52} - 17q^{53} - 10q^{54} + 21q^{55} + 9q^{56} - 32q^{57} + 87q^{58} + 38q^{59} - 45q^{60} + 23q^{61} + q^{62} + 6q^{63} - 75q^{64} - 75q^{65} + 61q^{66} + 5q^{67} + 88q^{68} + 13q^{69} - 18q^{70} + 8q^{71} + 13q^{72} + 90q^{73} + 79q^{74} - 18q^{75} - 85q^{76} - 10q^{77} - 18q^{78} - 6q^{79} - 147q^{80} - 6q^{81} + 112q^{82} - 90q^{83} - 3q^{84} + 55q^{85} - 8q^{86} - 10q^{87} - 210q^{88} - 15q^{89} - 4q^{90} - 22q^{91} + 39q^{92} + 50q^{93} + 144q^{94} + 72q^{95} + 7q^{96} - 48q^{97} - q^{98} - q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
64.1 −1.87100 0.549377i 0.654861 0.755750i 1.51634 + 0.974491i −0.563341 + 3.91812i −1.64044 + 1.05425i −0.415415 0.909632i 0.252236 + 0.291095i −0.142315 0.989821i 3.20654 7.02134i
64.2 −1.43941 0.422649i 0.654861 0.755750i 0.210759 + 0.135447i 0.271386 1.88753i −1.26203 + 0.811057i −0.415415 0.909632i 1.71869 + 1.98348i −0.142315 0.989821i −1.18840 + 2.60223i
64.3 0.345617 + 0.101482i 0.654861 0.755750i −1.57335 1.01113i −0.475765 + 3.30902i 0.303026 0.194743i −0.415415 0.909632i −0.912937 1.05359i −0.142315 0.989821i −0.500239 + 1.09537i
64.4 0.888980 + 0.261028i 0.654861 0.755750i −0.960357 0.617184i 0.251813 1.75140i 0.779430 0.500909i −0.415415 0.909632i −1.90611 2.19976i −0.142315 0.989821i 0.681020 1.49123i
64.5 1.81443 + 0.532766i 0.654861 0.755750i 1.32583 + 0.852056i 0.289215 2.01153i 1.59084 1.02237i −0.415415 0.909632i −0.525052 0.605943i −0.142315 0.989821i 1.59644 3.49571i
64.6 2.47754 + 0.727473i 0.654861 0.755750i 3.92650 + 2.52341i −0.135670 + 0.943603i 2.17223 1.39601i −0.415415 0.909632i 4.51049 + 5.20538i −0.142315 0.989821i −1.02257 + 2.23912i
85.1 −1.56944 + 1.81123i −0.841254 + 0.540641i −0.532780 3.70557i 1.21760 + 2.66617i 0.341071 2.37220i 0.959493 0.281733i 3.51550 + 2.25928i 0.415415 0.909632i −6.73999 1.97904i
85.2 −1.10975 + 1.28072i −0.841254 + 0.540641i −0.124067 0.862907i −0.209554 0.458859i 0.241171 1.67738i 0.959493 0.281733i −1.60841 1.03366i 0.415415 0.909632i 0.820221 + 0.240839i
85.3 −0.476363 + 0.549752i −0.841254 + 0.540641i 0.209324 + 1.45588i −1.25822 2.75513i 0.103524 0.720022i 0.959493 0.281733i −2.12399 1.36500i 0.415415 0.909632i 2.11401 + 0.620729i
85.4 0.451295 0.520822i −0.841254 + 0.540641i 0.217041 + 1.50955i 0.918881 + 2.01207i −0.0980757 + 0.682131i 0.959493 0.281733i 2.04365 + 1.31337i 0.415415 0.909632i 1.46262 + 0.429463i
85.5 0.767372 0.885594i −0.841254 + 0.540641i 0.0892119 + 0.620482i −1.61200 3.52979i −0.166766 + 1.15988i 0.959493 0.281733i 2.58953 + 1.66419i 0.415415 0.909632i −4.36297 1.28108i
85.6 1.48993 1.71948i −0.841254 + 0.540641i −0.452064 3.14417i 1.32209 + 2.89498i −0.323794 + 2.25204i 0.959493 0.281733i −2.25185 1.44718i 0.415415 0.909632i 6.94768 + 2.04002i
127.1 −2.26640 + 1.45653i 0.142315 0.989821i 2.18428 4.78290i 3.84207 1.12813i 1.11916 + 2.45062i 0.654861 + 0.755750i 1.24916 + 8.68812i −0.959493 0.281733i −7.06452 + 8.15290i
127.2 −1.70473 + 1.09556i 0.142315 0.989821i 0.875006 1.91600i −0.251997 + 0.0739930i 0.841802 + 1.84329i 0.654861 + 0.755750i 0.0306675 + 0.213297i −0.959493 0.281733i 0.348522 0.402215i
127.3 −0.539950 + 0.347005i 0.142315 0.989821i −0.659696 + 1.44453i −3.99137 + 1.17197i 0.266630 + 0.583838i 0.654861 + 0.755750i −0.327744 2.27951i −0.959493 0.281733i 1.74846 2.01783i
127.4 0.486928 0.312930i 0.142315 0.989821i −0.691656 + 1.51452i −1.52427 + 0.447565i −0.240447 0.526506i 0.654861 + 0.755750i 0.301897 + 2.09974i −0.959493 0.281733i −0.602152 + 0.694921i
127.5 0.978856 0.629072i 0.142315 0.989821i −0.268403 + 0.587721i 2.45426 0.720637i −0.483364 1.05842i 0.654861 + 0.755750i 0.438177 + 3.04759i −0.959493 0.281733i 1.94904 2.24931i
127.6 1.96460 1.26257i 0.142315 0.989821i 1.43472 3.14161i 0.650234 0.190926i −0.970126 2.12428i 0.654861 + 0.755750i −0.483142 3.36033i −0.959493 0.281733i 1.03639 1.19606i
169.1 −0.322450 + 2.24269i −0.415415 0.909632i −3.00670 0.882847i −0.335539 0.387233i 2.17397 0.638336i −0.841254 0.540641i 1.06701 2.33642i −0.654861 + 0.755750i 0.976638 0.627647i
169.2 −0.222029 + 1.54425i −0.415415 0.909632i −0.416411 0.122269i −2.19333 2.53124i 1.49693 0.439538i −0.841254 0.540641i −1.01493 + 2.22239i −0.654861 + 0.755750i 4.39584 2.82504i
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 463.6
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 483.2.q.e 60
23.c even 11 1 inner 483.2.q.e 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.q.e 60 1.a even 1 1 trivial
483.2.q.e 60 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{60} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(483, [\chi])\).