Properties

Label 2880.2.bl.c
Level $2880$
Weight $2$
Character orbit 2880.bl
Analytic conductor $22.997$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

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

\(\operatorname{Tr}(f)(q) = \) \( 32q + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q + 8q^{19} - 32q^{49} + 16q^{55} + 16q^{61} - 16q^{67} + 16q^{85} + 16q^{91} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
431.1 0 0 0 −0.707107 0.707107i 0 3.01345 0 0 0
431.2 0 0 0 −0.707107 0.707107i 0 −3.83891 0 0 0
431.3 0 0 0 −0.707107 0.707107i 0 −0.841567 0 0 0
431.4 0 0 0 −0.707107 0.707107i 0 −2.45331 0 0 0
431.5 0 0 0 −0.707107 0.707107i 0 1.80170 0 0 0
431.6 0 0 0 −0.707107 0.707107i 0 −1.44621 0 0 0
431.7 0 0 0 −0.707107 0.707107i 0 3.46834 0 0 0
431.8 0 0 0 −0.707107 0.707107i 0 0.296505 0 0 0
431.9 0 0 0 0.707107 + 0.707107i 0 3.46834 0 0 0
431.10 0 0 0 0.707107 + 0.707107i 0 −0.841567 0 0 0
431.11 0 0 0 0.707107 + 0.707107i 0 −3.83891 0 0 0
431.12 0 0 0 0.707107 + 0.707107i 0 −1.44621 0 0 0
431.13 0 0 0 0.707107 + 0.707107i 0 3.01345 0 0 0
431.14 0 0 0 0.707107 + 0.707107i 0 1.80170 0 0 0
431.15 0 0 0 0.707107 + 0.707107i 0 −2.45331 0 0 0
431.16 0 0 0 0.707107 + 0.707107i 0 0.296505 0 0 0
1871.1 0 0 0 −0.707107 + 0.707107i 0 3.01345 0 0 0
1871.2 0 0 0 −0.707107 + 0.707107i 0 −3.83891 0 0 0
1871.3 0 0 0 −0.707107 + 0.707107i 0 −0.841567 0 0 0
1871.4 0 0 0 −0.707107 + 0.707107i 0 −2.45331 0 0 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1871.16
Significant digits:
Format:

Inner twists

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{8} - 24 T_{7}^{6} + 164 T_{7}^{4} + 32 T_{7}^{3} - 320 T_{7}^{2} - 128 T_{7} + 64 \) acting on \(S_{2}^{\mathrm{new}}(2880, [\chi])\).