# Properties

 Label 2880.2.u.a Level $2880$ Weight $2$ Character orbit 2880.u Analytic conductor $22.997$ Analytic rank $0$ Dimension $96$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2880 = 2^{6} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2880.u (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$22.9969157821$$ Analytic rank: $$0$$ Dimension: $$96$$ Relative dimension: $$48$$ over $$\Q(i)$$ Twist minimal: no (minimal twist has level 720) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$96q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$96q + 16q^{19} - 96q^{49} - 64q^{55} - 32q^{61} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
719.1 0 0 0 −2.23581 + 0.0342493i 0 4.97879i 0 0 0
719.2 0 0 0 −2.22047 + 0.263678i 0 2.95946i 0 0 0
719.3 0 0 0 −2.21921 0.274088i 0 1.32258i 0 0 0
719.4 0 0 0 −2.19631 0.419806i 0 0.263783i 0 0 0
719.5 0 0 0 −2.18619 0.469629i 0 2.94937i 0 0 0
719.6 0 0 0 −2.14049 + 0.646750i 0 0.594230i 0 0 0
719.7 0 0 0 −1.93984 1.11222i 0 1.78786i 0 0 0
719.8 0 0 0 −1.91479 1.15480i 0 3.02955i 0 0 0
719.9 0 0 0 −1.81012 + 1.31281i 0 1.40695i 0 0 0
719.10 0 0 0 −1.73123 1.41522i 0 3.80565i 0 0 0
719.11 0 0 0 −1.71042 + 1.44030i 0 2.04714i 0 0 0
719.12 0 0 0 −1.65197 + 1.50698i 0 4.30751i 0 0 0
719.13 0 0 0 −1.50698 + 1.65197i 0 4.30751i 0 0 0
719.14 0 0 0 −1.44030 + 1.71042i 0 2.04714i 0 0 0
719.15 0 0 0 −1.41522 1.73123i 0 3.80565i 0 0 0
719.16 0 0 0 −1.31281 + 1.81012i 0 1.40695i 0 0 0
719.17 0 0 0 −1.15480 1.91479i 0 3.02955i 0 0 0
719.18 0 0 0 −1.11222 1.93984i 0 1.78786i 0 0 0
719.19 0 0 0 −0.646750 + 2.14049i 0 0.594230i 0 0 0
719.20 0 0 0 −0.469629 2.18619i 0 2.94937i 0 0 0
See all 96 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 2159.48 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
15.d odd 2 1 inner
16.f odd 4 1 inner
48.k even 4 1 inner
80.k odd 4 1 inner
240.t even 4 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2880.2.u.a 96
3.b odd 2 1 inner 2880.2.u.a 96
4.b odd 2 1 720.2.u.a 96
5.b even 2 1 inner 2880.2.u.a 96
12.b even 2 1 720.2.u.a 96
15.d odd 2 1 inner 2880.2.u.a 96
16.e even 4 1 720.2.u.a 96
16.f odd 4 1 inner 2880.2.u.a 96
20.d odd 2 1 720.2.u.a 96
48.i odd 4 1 720.2.u.a 96
48.k even 4 1 inner 2880.2.u.a 96
60.h even 2 1 720.2.u.a 96
80.k odd 4 1 inner 2880.2.u.a 96
80.q even 4 1 720.2.u.a 96
240.t even 4 1 inner 2880.2.u.a 96
240.bm odd 4 1 720.2.u.a 96

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
720.2.u.a 96 4.b odd 2 1
720.2.u.a 96 12.b even 2 1
720.2.u.a 96 16.e even 4 1
720.2.u.a 96 20.d odd 2 1
720.2.u.a 96 48.i odd 4 1
720.2.u.a 96 60.h even 2 1
720.2.u.a 96 80.q even 4 1
720.2.u.a 96 240.bm odd 4 1
2880.2.u.a 96 1.a even 1 1 trivial
2880.2.u.a 96 3.b odd 2 1 inner
2880.2.u.a 96 5.b even 2 1 inner
2880.2.u.a 96 15.d odd 2 1 inner
2880.2.u.a 96 16.f odd 4 1 inner
2880.2.u.a 96 48.k even 4 1 inner
2880.2.u.a 96 80.k odd 4 1 inner
2880.2.u.a 96 240.t even 4 1 inner

## Hecke kernels

This newform subspace is the entire newspace $$S_{2}^{\mathrm{new}}(2880, [\chi])$$.