Properties

Label 483.2.e.a
Level $483$
Weight $2$
Character orbit 483.e
Analytic conductor $3.857$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48q - 4q^{3} - 40q^{4} + 6q^{6} + 4q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 48q - 4q^{3} - 40q^{4} + 6q^{6} + 4q^{9} + 22q^{12} - 8q^{13} + 24q^{16} - 14q^{18} - 12q^{24} + 88q^{25} - 16q^{27} - 8q^{31} - 10q^{36} + 8q^{46} - 98q^{48} - 48q^{49} + 28q^{52} - 28q^{54} - 92q^{58} + 92q^{64} + 8q^{69} + 8q^{70} + 60q^{72} + 40q^{73} - 80q^{75} + 114q^{78} - 28q^{81} - 20q^{82} - 40q^{85} - 28q^{87} - 76q^{93} - 12q^{94} - 6q^{96} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
344.1 2.64103i −1.65834 + 0.499912i −4.97503 −2.97721 1.32028 + 4.37972i 1.00000i 7.85715i 2.50018 1.65805i 7.86291i
344.2 2.64103i −1.65834 + 0.499912i −4.97503 2.97721 1.32028 + 4.37972i 1.00000i 7.85715i 2.50018 1.65805i 7.86291i
344.3 2.35218i 1.12077 1.32055i −3.53277 −2.32116 −3.10619 2.63627i 1.00000i 3.60535i −0.487727 2.96009i 5.45980i
344.4 2.35218i 1.12077 1.32055i −3.53277 2.32116 −3.10619 2.63627i 1.00000i 3.60535i −0.487727 2.96009i 5.45980i
344.5 2.27845i −0.307505 + 1.70454i −3.19131 −0.401391 3.88369 + 0.700634i 1.00000i 2.71435i −2.81088 1.04831i 0.914548i
344.6 2.27845i −0.307505 + 1.70454i −3.19131 0.401391 3.88369 + 0.700634i 1.00000i 2.71435i −2.81088 1.04831i 0.914548i
344.7 2.26372i −1.42471 0.984983i −3.12443 −3.16242 −2.22973 + 3.22515i 1.00000i 2.54539i 1.05962 + 2.80664i 7.15884i
344.8 2.26372i −1.42471 0.984983i −3.12443 3.16242 −2.22973 + 3.22515i 1.00000i 2.54539i 1.05962 + 2.80664i 7.15884i
344.9 1.98227i 0.949942 + 1.44831i −1.92939 −4.16373 2.87095 1.88304i 1.00000i 0.139961i −1.19522 + 2.75163i 8.25364i
344.10 1.98227i 0.949942 + 1.44831i −1.92939 4.16373 2.87095 1.88304i 1.00000i 0.139961i −1.19522 + 2.75163i 8.25364i
344.11 1.67931i 1.72585 + 0.146449i −0.820088 −1.07520 0.245933 2.89824i 1.00000i 1.98144i 2.95711 + 0.505497i 1.80559i
344.12 1.67931i 1.72585 + 0.146449i −0.820088 1.07520 0.245933 2.89824i 1.00000i 1.98144i 2.95711 + 0.505497i 1.80559i
344.13 1.44207i 0.0348577 1.73170i −0.0795775 −2.43097 −2.49724 0.0502674i 1.00000i 2.76939i −2.99757 0.120726i 3.50564i
344.14 1.44207i 0.0348577 1.73170i −0.0795775 2.43097 −2.49724 0.0502674i 1.00000i 2.76939i −2.99757 0.120726i 3.50564i
344.15 1.06181i −1.10086 + 1.33720i 0.872554 −4.21218 1.41986 + 1.16891i 1.00000i 3.05011i −0.576205 2.94414i 4.47255i
344.16 1.06181i −1.10086 + 1.33720i 0.872554 4.21218 1.41986 + 1.16891i 1.00000i 3.05011i −0.576205 2.94414i 4.47255i
344.17 0.800018i −1.73165 0.0370806i 1.35997 −1.73737 −0.0296651 + 1.38535i 1.00000i 2.68804i 2.99725 + 0.128422i 1.38993i
344.18 0.800018i −1.73165 0.0370806i 1.35997 1.73737 −0.0296651 + 1.38535i 1.00000i 2.68804i 2.99725 + 0.128422i 1.38993i
344.19 0.548382i 1.56357 0.745160i 1.69928 −2.39464 −0.408632 0.857431i 1.00000i 2.02862i 1.88947 2.33021i 1.31318i
344.20 0.548382i 1.56357 0.745160i 1.69928 2.39464 −0.408632 0.857431i 1.00000i 2.02862i 1.88947 2.33021i 1.31318i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 344.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
23.b odd 2 1 inner
69.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.2.e.a 48
3.b odd 2 1 inner 483.2.e.a 48
23.b odd 2 1 inner 483.2.e.a 48
69.c even 2 1 inner 483.2.e.a 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.e.a 48 1.a even 1 1 trivial
483.2.e.a 48 3.b odd 2 1 inner
483.2.e.a 48 23.b odd 2 1 inner
483.2.e.a 48 69.c even 2 1 inner

Hecke kernels

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