Properties

Label 483.2.q.d
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.

\(\operatorname{Tr}(f)(q) = \) \( 60q - q^{2} + 6q^{3} - 3q^{4} - 13q^{5} + 12q^{6} - 6q^{7} + 25q^{8} - 6q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 60q - q^{2} + 6q^{3} - 3q^{4} - 13q^{5} + 12q^{6} - 6q^{7} + 25q^{8} - 6q^{9} + 5q^{11} + 3q^{12} + 22q^{13} - q^{14} + 2q^{15} - 27q^{16} + q^{17} - q^{18} + 20q^{19} - 75q^{20} + 6q^{21} - 16q^{22} - 9q^{23} - 36q^{24} - 15q^{25} - 16q^{26} + 6q^{27} - 14q^{28} - 3q^{29} + 17q^{31} - 73q^{32} - 5q^{33} + 55q^{34} - 2q^{35} - 14q^{36} + 56q^{37} - 22q^{38} - 22q^{39} - 37q^{40} - 18q^{41} + 12q^{42} - 19q^{43} - 12q^{44} + 20q^{45} - 45q^{46} + 42q^{47} - 28q^{48} - 6q^{49} - 42q^{50} - q^{51} + 76q^{52} - 11q^{53} - 10q^{54} - 61q^{55} + 3q^{56} + 24q^{57} - 78q^{58} + 38q^{59} + 31q^{60} + 5q^{61} + 69q^{62} - 6q^{63} - 27q^{64} + 51q^{65} + 49q^{66} - 27q^{67} + 112q^{68} - 13q^{69} + 22q^{70} - 4q^{71} + 25q^{72} + 48q^{73} - 62q^{74} + 26q^{75} - 85q^{76} - 28q^{77} - 6q^{78} - 6q^{79} + 169q^{80} - 6q^{81} - 200q^{82} - 6q^{83} + 3q^{84} - 21q^{85} - 180q^{86} + 14q^{87} + 211q^{88} - 57q^{89} - 22q^{91} + 49q^{92} - 50q^{93} + 16q^{94} + 56q^{95} + 7q^{96} - 52q^{97} - 12q^{98} + 5q^{99} + O(q^{100}) \)

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 −2.35051 0.690173i 0.654861 0.755750i 3.36607 + 2.16324i −0.0495443 + 0.344588i −2.06086 + 1.32443i 0.415415 + 0.909632i −3.21050 3.70511i −0.142315 0.989821i 0.354280 0.775765i
64.2 −1.03092 0.302706i 0.654861 0.755750i −0.711340 0.457151i −0.107286 + 0.746189i −0.903879 + 0.580888i 0.415415 + 0.909632i 2.00217 + 2.31063i −0.142315 0.989821i 0.336479 0.736786i
64.3 −0.0618105 0.0181492i 0.654861 0.755750i −1.67902 1.07904i −0.424340 + 2.95135i −0.0541936 + 0.0348281i 0.415415 + 0.909632i 0.168569 + 0.194540i −0.142315 0.989821i 0.0797933 0.174723i
64.4 1.04309 + 0.306279i 0.654861 0.755750i −0.688274 0.442327i 0.159962 1.11256i 0.914550 0.587746i 0.415415 + 0.909632i −2.00629 2.31538i −0.142315 0.989821i 0.507608 1.11151i
64.5 2.07162 + 0.608284i 0.654861 0.755750i 2.23911 + 1.43899i −0.483629 + 3.36371i 1.81634 1.16729i 0.415415 + 0.909632i 0.935489 + 1.07961i −0.142315 0.989821i −3.04799 + 6.67417i
64.6 2.24006 + 0.657740i 0.654861 0.755750i 2.90273 + 1.86547i 0.461461 3.20953i 1.96401 1.26219i 0.415415 + 0.909632i 2.21758 + 2.55922i −0.142315 0.989821i 3.14474 6.88602i
85.1 −1.76537 + 2.03734i −0.841254 + 0.540641i −0.749611 5.21366i −1.11741 2.44678i 0.383651 2.66835i −0.959493 + 0.281733i 7.40965 + 4.76189i 0.415415 0.909632i 6.95754 + 2.04292i
85.2 −1.19069 + 1.37413i −0.841254 + 0.540641i −0.185857 1.29267i −0.605948 1.32684i 0.258761 1.79972i −0.959493 + 0.281733i −1.06160 0.682248i 0.415415 0.909632i 2.54474 + 0.747203i
85.3 −1.03904 + 1.19912i −0.841254 + 0.540641i −0.0736471 0.512227i 0.945752 + 2.07091i 0.225805 1.57051i −0.959493 + 0.281733i −1.97883 1.27171i 0.415415 0.909632i −3.46594 1.01769i
85.4 −0.247496 + 0.285625i −0.841254 + 0.540641i 0.264302 + 1.83826i 1.62071 + 3.54886i 0.0537860 0.374090i −0.959493 + 0.281733i −1.22635 0.788126i 0.415415 0.909632i −1.41476 0.415412i
85.5 0.765301 0.883205i −0.841254 + 0.540641i 0.0902651 + 0.627808i −0.487321 1.06708i −0.166316 + 1.15675i −0.959493 + 0.281733i 2.58982 + 1.66438i 0.415415 0.909632i −1.31540 0.386237i
85.6 1.53423 1.77059i −0.841254 + 0.540641i −0.496516 3.45335i −0.667274 1.46113i −0.333420 + 2.31898i −0.959493 + 0.281733i −2.93441 1.88583i 0.415415 0.909632i −3.61081 1.06023i
127.1 −2.13310 + 1.37086i 0.142315 0.989821i 1.84002 4.02908i −1.89262 + 0.555724i 1.05333 + 2.30648i −0.654861 0.755750i 0.876645 + 6.09720i −0.959493 0.281733i 3.27533 3.77993i
127.2 −1.49352 + 0.959824i 0.142315 0.989821i 0.478496 1.04776i 1.94954 0.572436i 0.737505 + 1.61491i −0.654861 0.755750i −0.214292 1.49043i −0.959493 0.281733i −2.36223 + 2.72616i
127.3 −0.502226 + 0.322761i 0.142315 0.989821i −0.682774 + 1.49507i −0.741298 + 0.217665i 0.248001 + 0.543047i −0.654861 0.755750i −0.309565 2.15307i −0.959493 0.281733i 0.302045 0.348578i
127.4 −0.112067 + 0.0720210i 0.142315 0.989821i −0.823458 + 1.80312i −0.784721 + 0.230415i 0.0553392 + 0.121176i −0.654861 0.755750i −0.0754970 0.525093i −0.959493 0.281733i 0.0713466 0.0823383i
127.5 1.84770 1.18744i 0.142315 0.989821i 1.17314 2.56882i 2.35208 0.690633i −0.912403 1.99788i −0.654861 0.755750i −0.257569 1.79143i −0.959493 0.281733i 3.52585 4.06905i
127.6 2.29607 1.47560i 0.142315 0.989821i 2.26374 4.95689i −3.38655 + 0.994380i −1.13381 2.48270i −0.654861 0.755750i −1.33981 9.31861i −0.959493 0.281733i −6.30846 + 7.28035i
169.1 −0.401532 + 2.79272i −0.415415 0.909632i −5.71907 1.67927i −1.39224 1.60673i 2.70715 0.794891i 0.841254 + 0.540641i 4.64198 10.1645i −0.654861 + 0.755750i 5.04616 3.24297i
169.2 −0.275145 + 1.91367i −0.415415 0.909632i −1.66745 0.489608i −1.20808 1.39419i 1.85504 0.544688i 0.841254 + 0.540641i −0.210547 + 0.461033i −0.654861 + 0.755750i 3.00043 1.92826i
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.d 60
23.c even 11 1 inner 483.2.q.d 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.q.d 60 1.a even 1 1 trivial
483.2.q.d 60 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(14\!\cdots\!39\)\( T_{2}^{26} + \)\(15\!\cdots\!87\)\( T_{2}^{25} + \)\(24\!\cdots\!97\)\( T_{2}^{24} + \)\(22\!\cdots\!68\)\( T_{2}^{23} + \)\(23\!\cdots\!46\)\( T_{2}^{22} + \)\(20\!\cdots\!50\)\( T_{2}^{21} + \)\(13\!\cdots\!12\)\( T_{2}^{20} + 951741265125 T_{2}^{19} + 626157593652 T_{2}^{18} + 215694456076 T_{2}^{17} + \)\(23\!\cdots\!67\)\( T_{2}^{16} + \)\(21\!\cdots\!81\)\( T_{2}^{15} + \)\(50\!\cdots\!31\)\( T_{2}^{14} + \)\(63\!\cdots\!16\)\( T_{2}^{13} + \)\(62\!\cdots\!26\)\( T_{2}^{12} + \)\(56\!\cdots\!51\)\( T_{2}^{11} + \)\(46\!\cdots\!10\)\( T_{2}^{10} + \)\(29\!\cdots\!13\)\( T_{2}^{9} + \)\(14\!\cdots\!84\)\( T_{2}^{8} + 558898220619 T_{2}^{7} + 167568971697 T_{2}^{6} + 38355862851 T_{2}^{5} + 6655533804 T_{2}^{4} + 822987783 T_{2}^{3} + 66718809 T_{2}^{2} + 3050865 T_{2} + 59049 \)">\(T_{2}^{60} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(483, [\chi])\).