# 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 $2$

# Related objects

## 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.

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

## 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: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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