Properties

Label 483.3.g.a
Level $483$
Weight $3$
Character orbit 483.g
Analytic conductor $13.161$
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: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 60q + 128q^{4} - 16q^{7} + 24q^{8} - 180q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 60q + 128q^{4} - 16q^{7} + 24q^{8} - 180q^{9} + 28q^{14} - 48q^{15} + 192q^{16} + 48q^{21} - 8q^{22} - 292q^{25} - 128q^{28} + 136q^{29} + 96q^{32} - 88q^{35} - 384q^{36} - 200q^{37} + 48q^{39} - 60q^{42} + 72q^{43} + 352q^{44} + 132q^{49} - 376q^{50} - 112q^{53} + 260q^{56} - 240q^{57} + 32q^{58} - 216q^{60} + 48q^{63} + 536q^{64} - 8q^{65} - 408q^{67} - 112q^{70} + 456q^{71} - 72q^{72} - 120q^{74} + 104q^{77} + 48q^{78} + 192q^{79} + 540q^{81} + 24q^{84} + 488q^{85} + 72q^{86} + 432q^{88} + 88q^{91} + 48q^{93} + 880q^{95} - 16q^{98} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
139.1 −3.94080 1.73205i 11.5299 1.76571i 6.82566i −5.04591 4.85168i −29.6737 −3.00000 6.95831i
139.2 −3.94080 1.73205i 11.5299 1.76571i 6.82566i −5.04591 + 4.85168i −29.6737 −3.00000 6.95831i
139.3 −3.48909 1.73205i 8.17374 1.46096i 6.04328i 6.91536 1.08528i −14.5626 −3.00000 5.09743i
139.4 −3.48909 1.73205i 8.17374 1.46096i 6.04328i 6.91536 + 1.08528i −14.5626 −3.00000 5.09743i
139.5 −3.29495 1.73205i 6.85669 6.17562i 5.70702i −6.91716 + 1.07376i −9.41266 −3.00000 20.3484i
139.6 −3.29495 1.73205i 6.85669 6.17562i 5.70702i −6.91716 1.07376i −9.41266 −3.00000 20.3484i
139.7 −3.28514 1.73205i 6.79214 3.80523i 5.69003i −0.993207 + 6.92918i −9.17258 −3.00000 12.5007i
139.8 −3.28514 1.73205i 6.79214 3.80523i 5.69003i −0.993207 6.92918i −9.17258 −3.00000 12.5007i
139.9 −3.13389 1.73205i 5.82124 7.50145i 5.42805i 4.32864 5.50117i −5.70757 −3.00000 23.5087i
139.10 −3.13389 1.73205i 5.82124 7.50145i 5.42805i 4.32864 + 5.50117i −5.70757 −3.00000 23.5087i
139.11 −2.79612 1.73205i 3.81828 8.09762i 4.84302i −5.87622 + 3.80395i 0.508111 −3.00000 22.6419i
139.12 −2.79612 1.73205i 3.81828 8.09762i 4.84302i −5.87622 3.80395i 0.508111 −3.00000 22.6419i
139.13 −2.51134 1.73205i 2.30684 3.95129i 4.34977i −0.923197 + 6.93885i 4.25211 −3.00000 9.92304i
139.14 −2.51134 1.73205i 2.30684 3.95129i 4.34977i −0.923197 6.93885i 4.25211 −3.00000 9.92304i
139.15 −2.20043 1.73205i 0.841896 0.777779i 3.81126i 2.99585 6.32652i 6.94919 −3.00000 1.71145i
139.16 −2.20043 1.73205i 0.841896 0.777779i 3.81126i 2.99585 + 6.32652i 6.94919 −3.00000 1.71145i
139.17 −2.01661 1.73205i 0.0667068 2.33922i 3.49287i −5.55691 + 4.25685i 7.93191 −3.00000 4.71728i
139.18 −2.01661 1.73205i 0.0667068 2.33922i 3.49287i −5.55691 4.25685i 7.93191 −3.00000 4.71728i
139.19 −1.79815 1.73205i −0.766656 9.01598i 3.11449i 6.86887 1.34858i 8.57116 −3.00000 16.2121i
139.20 −1.79815 1.73205i −0.766656 9.01598i 3.11449i 6.86887 + 1.34858i 8.57116 −3.00000 16.2121i
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 139.60
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.3.g.a 60
7.b odd 2 1 inner 483.3.g.a 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.3.g.a 60 1.a even 1 1 trivial
483.3.g.a 60 7.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(483, [\chi])\).