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Properties

Label 8280.2.p.a
Level $8280$
Weight $2$
Character orbit 8280.p
Analytic conductor $66.116$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.p (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(66.1161328736\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 48 q^{5} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 48 q - 48 q^{5} - 8 q^{11} + 4 q^{23} + 48 q^{25} + 8 q^{31} - 32 q^{49} + 8 q^{55} - 16 q^{73} - 32 q^{83} - 8 q^{89} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1241.1 0 0 0 −1.00000 0 − 4.92948i 0 0 0
1241.2 0 0 0 −1.00000 0 − 4.64793i 0 0 0
1241.3 0 0 0 −1.00000 0 − 4.29385i 0 0 0
1241.4 0 0 0 −1.00000 0 − 3.83098i 0 0 0
1241.5 0 0 0 −1.00000 0 − 3.49780i 0 0 0
1241.6 0 0 0 −1.00000 0 − 3.21237i 0 0 0
1241.7 0 0 0 −1.00000 0 − 3.18371i 0 0 0
1241.8 0 0 0 −1.00000 0 − 3.13239i 0 0 0
1241.9 0 0 0 −1.00000 0 − 3.11398i 0 0 0
1241.10 0 0 0 −1.00000 0 − 2.84853i 0 0 0
1241.11 0 0 0 −1.00000 0 − 2.78247i 0 0 0
1241.12 0 0 0 −1.00000 0 − 2.72943i 0 0 0
1241.13 0 0 0 −1.00000 0 − 2.53343i 0 0 0
1241.14 0 0 0 −1.00000 0 − 2.35143i 0 0 0
1241.15 0 0 0 −1.00000 0 − 2.09276i 0 0 0
1241.16 0 0 0 −1.00000 0 − 2.08780i 0 0 0
1241.17 0 0 0 −1.00000 0 − 1.46186i 0 0 0
1241.18 0 0 0 −1.00000 0 − 1.44649i 0 0 0
1241.19 0 0 0 −1.00000 0 − 1.36101i 0 0 0
1241.20 0 0 0 −1.00000 0 − 1.20278i 0 0 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1241.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
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 8280.2.p.a ✓ 48
3.b odd 2 1 8280.2.p.b yes 48
23.b odd 2 1 8280.2.p.b yes 48
69.c even 2 1 inner 8280.2.p.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8280.2.p.a ✓ 48 1.a even 1 1 trivial
8280.2.p.a ✓ 48 69.c even 2 1 inner
8280.2.p.b yes 48 3.b odd 2 1
8280.2.p.b yes 48 23.b odd 2 1