Properties

Label 483.2.n.a
Level $483$
Weight $2$
Character orbit 483.n
Analytic conductor $3.857$
Analytic rank $0$
Dimension $116$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(116\)
Relative dimension: \(58\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 116q + 56q^{4} - 10q^{7} - 4q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 116q + 56q^{4} - 10q^{7} - 4q^{9} - 12q^{10} - 30q^{12} + 20q^{15} - 52q^{16} - 10q^{18} + 6q^{19} - 6q^{21} - 16q^{22} - 66q^{25} + 16q^{28} - 32q^{30} - 42q^{31} - 30q^{33} + 8q^{36} - 2q^{37} - 22q^{39} - 36q^{40} + 46q^{42} + 20q^{43} + 30q^{45} - 22q^{49} + 12q^{51} + 48q^{52} - 54q^{54} - 44q^{57} + 52q^{58} + 32q^{60} + 36q^{61} - 38q^{63} - 160q^{64} + 10q^{67} - 20q^{70} + 62q^{72} + 18q^{73} + 78q^{75} + 12q^{78} + 10q^{79} - 28q^{81} + 32q^{84} - 32q^{85} - 30q^{87} - 36q^{88} + 50q^{91} + 60q^{94} + 84q^{96} + 24q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
47.1 −2.44467 1.41143i 1.69781 0.342692i 2.98426 + 5.16889i 0.950213 1.64582i −4.63427 1.55857i −1.23167 2.34158i 11.2026i 2.76512 1.16365i −4.64591 + 2.68232i
47.2 −2.33544 1.34837i −1.04040 + 1.38476i 2.63619 + 4.56602i −0.0332776 + 0.0576385i 4.29696 1.83120i −1.58536 + 2.11817i 8.82477i −0.835146 2.88141i 0.155436 0.0897409i
47.3 −2.29312 1.32393i −1.35264 1.08184i 2.50559 + 4.33981i −2.05000 + 3.55071i 1.66947 + 4.27158i −0.0386680 2.64547i 7.97318i 0.659249 + 2.92667i 9.40179 5.42813i
47.4 −2.13598 1.23321i −1.67324 + 0.447500i 2.04161 + 3.53618i 1.36168 2.35849i 4.12588 + 1.10761i 2.39415 1.12607i 5.13811i 2.59949 1.49755i −5.81703 + 3.35846i
47.5 −2.09741 1.21094i 1.21100 + 1.23833i 1.93276 + 3.34764i −0.868774 + 1.50476i −1.04042 4.06375i 2.64399 0.0966161i 4.51808i −0.0669439 + 2.99925i 3.64436 2.10407i
47.6 −2.01952 1.16597i 0.890949 + 1.48533i 1.71897 + 2.97735i 1.28353 2.22314i −0.0674375 4.03848i −0.527114 + 2.59271i 3.35320i −1.41242 + 2.64671i −5.18423 + 2.99312i
47.7 −1.95986 1.13153i −1.38096 1.04545i 1.56071 + 2.70323i 0.105593 0.182893i 1.52353 + 3.61153i 1.41527 + 2.23540i 2.53784i 0.814080 + 2.88743i −0.413897 + 0.238964i
47.8 −1.94838 1.12490i 0.249841 1.71394i 1.53079 + 2.65141i −0.341657 + 0.591768i −2.41479 + 3.05836i −2.51638 + 0.817220i 2.38836i −2.87516 0.856422i 1.33136 0.768660i
47.9 −1.85789 1.07265i −0.419028 + 1.68060i 1.30116 + 2.25367i −0.826951 + 1.43232i 2.58120 2.67289i −0.559247 2.58597i 1.29215i −2.64883 1.40844i 3.07276 1.77406i
47.10 −1.81419 1.04742i −0.759538 1.55663i 1.19418 + 2.06838i 1.94488 3.36863i −0.252504 + 3.61957i −0.829752 2.51227i 0.813554i −1.84620 + 2.36464i −7.05676 + 4.07422i
47.11 −1.75262 1.01188i 1.45057 0.946485i 1.04778 + 1.81482i 1.57777 2.73277i −3.50003 + 0.191028i 1.90338 + 1.83770i 0.193410i 1.20833 2.74589i −5.53045 + 3.19301i
47.12 −1.61162 0.930468i −1.59984 + 0.663721i 0.731543 + 1.26707i −2.09187 + 3.62322i 3.19590 + 0.418931i 0.0287355 + 2.64560i 0.999164i 2.11895 2.12369i 6.74259 3.89284i
47.13 −1.56218 0.901925i 1.68751 + 0.390253i 0.626938 + 1.08589i −0.604515 + 1.04705i −2.28422 2.13166i −2.35039 1.21476i 1.34590i 2.69541 + 1.31711i 1.88872 1.09045i
47.14 −1.40944 0.813741i 1.19429 1.25446i 0.324350 + 0.561790i −0.349118 + 0.604691i −2.70409 + 0.796242i 0.554890 2.58691i 2.19922i −0.147336 2.99638i 0.984123 0.568184i
47.15 −1.33899 0.773067i −1.69734 0.345005i 0.195266 + 0.338210i 0.489073 0.847100i 2.00602 + 1.77412i −2.35128 + 1.21304i 2.48845i 2.76194 + 1.17118i −1.30973 + 0.756173i
47.16 −1.18271 0.682837i −1.09928 + 1.33850i −0.0674665 0.116855i 1.64053 2.84148i 2.21410 0.832434i −2.62678 0.316234i 2.91562i −0.583186 2.94277i −3.88054 + 2.24043i
47.17 −1.08140 0.624349i −0.486586 + 1.66230i −0.220377 0.381705i 1.03800 1.79786i 1.56405 1.49382i 2.55312 + 0.693956i 3.04776i −2.52647 1.61770i −2.24498 + 1.29614i
47.18 −1.07338 0.619715i −0.722709 1.57407i −0.231907 0.401675i −0.273772 + 0.474187i −0.199734 + 2.13744i 2.55123 0.700882i 3.05372i −1.95538 + 2.27519i 0.587721 0.339321i
47.19 −1.06618 0.615560i 0.610600 + 1.62085i −0.242171 0.419452i −1.71746 + 2.97473i 0.346722 2.10399i −2.51610 + 0.818060i 3.05852i −2.25433 + 1.97939i 3.66225 2.11440i
47.20 −0.995717 0.574877i 1.25957 + 1.18890i −0.339032 0.587221i 1.31638 2.28004i −0.570703 1.90791i 1.26124 2.32579i 3.07912i 0.173032 + 2.99501i −2.62149 + 1.51352i
See next 80 embeddings (of 116 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 185.58
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.d odd 6 1 inner
21.g 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.n.a 116
3.b odd 2 1 inner 483.2.n.a 116
7.d odd 6 1 inner 483.2.n.a 116
21.g even 6 1 inner 483.2.n.a 116
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.n.a 116 1.a even 1 1 trivial
483.2.n.a 116 3.b odd 2 1 inner
483.2.n.a 116 7.d odd 6 1 inner
483.2.n.a 116 21.g even 6 1 inner

Hecke kernels

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