# Properties

 Label 2880.2.bc.a Level $2880$ Weight $2$ Character orbit 2880.bc Analytic conductor $22.997$ Analytic rank $0$ Dimension $96$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2880 = 2^{6} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2880.bc (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.

 $$\operatorname{Tr}(f)(q) =$$ $$96q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$96q - 16q^{19} - 64q^{43} + 32q^{61} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
593.1 0 0 0 −2.23567 + 0.0422885i 0 −1.80532 1.80532i 0 0 0
593.2 0 0 0 −2.23368 + 0.103242i 0 −1.05564 1.05564i 0 0 0
593.3 0 0 0 −2.21174 + 0.328918i 0 2.33595 + 2.33595i 0 0 0
593.4 0 0 0 −2.14437 0.633793i 0 −0.431588 0.431588i 0 0 0
593.5 0 0 0 −2.06437 + 0.859295i 0 1.97431 + 1.97431i 0 0 0
593.6 0 0 0 −2.04823 + 0.897076i 0 −3.15125 3.15125i 0 0 0
593.7 0 0 0 −2.02484 0.948701i 0 −1.06871 1.06871i 0 0 0
593.8 0 0 0 −1.98008 1.03889i 0 2.57554 + 2.57554i 0 0 0
593.9 0 0 0 −1.95867 + 1.07871i 0 −1.03362 1.03362i 0 0 0
593.10 0 0 0 −1.78433 + 1.34765i 0 3.52140 + 3.52140i 0 0 0
593.11 0 0 0 −1.74165 1.40237i 0 −2.18248 2.18248i 0 0 0
593.12 0 0 0 −1.73447 1.41125i 0 2.32146 + 2.32146i 0 0 0
593.13 0 0 0 −1.58807 1.57418i 0 0.639411 + 0.639411i 0 0 0
593.14 0 0 0 −1.29671 1.82168i 0 −2.16011 2.16011i 0 0 0
593.15 0 0 0 −1.29201 + 1.82503i 0 2.02860 + 2.02860i 0 0 0
593.16 0 0 0 −1.26609 + 1.84310i 0 −0.461154 0.461154i 0 0 0
593.17 0 0 0 −1.09255 + 1.95099i 0 1.70979 + 1.70979i 0 0 0
593.18 0 0 0 −1.08017 + 1.95786i 0 −0.362166 0.362166i 0 0 0
593.19 0 0 0 −0.885098 2.05344i 0 2.95475 + 2.95475i 0 0 0
593.20 0 0 0 −0.470363 2.18604i 0 0.177389 + 0.177389i 0 0 0
See all 96 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1457.48 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
80.i odd 4 1 inner
240.bb 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.bc.a 96
3.b odd 2 1 inner 2880.2.bc.a 96
4.b odd 2 1 720.2.bc.a 96
5.c odd 4 1 2880.2.bg.a 96
12.b even 2 1 720.2.bc.a 96
15.e even 4 1 2880.2.bg.a 96
16.e even 4 1 2880.2.bg.a 96
16.f odd 4 1 720.2.bg.a yes 96
20.e even 4 1 720.2.bg.a yes 96
48.i odd 4 1 2880.2.bg.a 96
48.k even 4 1 720.2.bg.a yes 96
60.l odd 4 1 720.2.bg.a yes 96
80.i odd 4 1 inner 2880.2.bc.a 96
80.s even 4 1 720.2.bc.a 96
240.z odd 4 1 720.2.bc.a 96
240.bb even 4 1 inner 2880.2.bc.a 96

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
720.2.bc.a 96 4.b odd 2 1
720.2.bc.a 96 12.b even 2 1
720.2.bc.a 96 80.s even 4 1
720.2.bc.a 96 240.z odd 4 1
720.2.bg.a yes 96 16.f odd 4 1
720.2.bg.a yes 96 20.e even 4 1
720.2.bg.a yes 96 48.k even 4 1
720.2.bg.a yes 96 60.l odd 4 1
2880.2.bc.a 96 1.a even 1 1 trivial
2880.2.bc.a 96 3.b odd 2 1 inner
2880.2.bc.a 96 80.i odd 4 1 inner
2880.2.bc.a 96 240.bb even 4 1 inner
2880.2.bg.a 96 5.c odd 4 1
2880.2.bg.a 96 15.e even 4 1
2880.2.bg.a 96 16.e even 4 1
2880.2.bg.a 96 48.i odd 4 1

## Hecke kernels

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