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

Downloads

Learn more about

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:

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 \(S_{2}^{\mathrm{new}}(2880, [\chi])\).