# Properties

 Label 2880.2.t.e Level $2880$ Weight $2$ Character orbit 2880.t Analytic conductor $22.997$ Analytic rank $0$ Dimension $32$ 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.t (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$22.9969157821$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$32q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$32q - 8q^{19} - 32q^{37} - 16q^{43} - 32q^{49} - 16q^{61} + 16q^{67} + 16q^{79} + 16q^{85} + 80q^{91} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
721.1 0 0 0 −0.707107 + 0.707107i 0 4.30899i 0 0 0
721.2 0 0 0 −0.707107 + 0.707107i 0 1.47784i 0 0 0
721.3 0 0 0 −0.707107 + 0.707107i 0 2.05446i 0 0 0
721.4 0 0 0 −0.707107 + 0.707107i 0 0.511707i 0 0 0
721.5 0 0 0 −0.707107 + 0.707107i 0 1.69880i 0 0 0
721.6 0 0 0 −0.707107 + 0.707107i 0 0.635963i 0 0 0
721.7 0 0 0 −0.707107 + 0.707107i 0 4.35099i 0 0 0
721.8 0 0 0 −0.707107 + 0.707107i 0 4.06749i 0 0 0
721.9 0 0 0 0.707107 0.707107i 0 2.05446i 0 0 0
721.10 0 0 0 0.707107 0.707107i 0 1.47784i 0 0 0
721.11 0 0 0 0.707107 0.707107i 0 0.511707i 0 0 0
721.12 0 0 0 0.707107 0.707107i 0 0.635963i 0 0 0
721.13 0 0 0 0.707107 0.707107i 0 1.69880i 0 0 0
721.14 0 0 0 0.707107 0.707107i 0 4.30899i 0 0 0
721.15 0 0 0 0.707107 0.707107i 0 4.06749i 0 0 0
721.16 0 0 0 0.707107 0.707107i 0 4.35099i 0 0 0
2161.1 0 0 0 −0.707107 0.707107i 0 4.30899i 0 0 0
2161.2 0 0 0 −0.707107 0.707107i 0 1.47784i 0 0 0
2161.3 0 0 0 −0.707107 0.707107i 0 2.05446i 0 0 0
2161.4 0 0 0 −0.707107 0.707107i 0 0.511707i 0 0 0
See all 32 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 2161.16 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
16.e even 4 1 inner
48.i odd 4 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2880.2.t.e 32
3.b odd 2 1 inner 2880.2.t.e 32
4.b odd 2 1 720.2.t.e 32
12.b even 2 1 720.2.t.e 32
16.e even 4 1 inner 2880.2.t.e 32
16.f odd 4 1 720.2.t.e 32
48.i odd 4 1 inner 2880.2.t.e 32
48.k even 4 1 720.2.t.e 32

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
720.2.t.e 32 4.b odd 2 1
720.2.t.e 32 12.b even 2 1
720.2.t.e 32 16.f odd 4 1
720.2.t.e 32 48.k even 4 1
2880.2.t.e 32 1.a even 1 1 trivial
2880.2.t.e 32 3.b odd 2 1 inner
2880.2.t.e 32 16.e even 4 1 inner
2880.2.t.e 32 48.i odd 4 1 inner

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{7}^{16} + \cdots$$ acting on $$S_{2}^{\mathrm{new}}(2880, [\chi])$$.