↑

Properties

Label 2880.2.bl.b
Level $2880$
Weight $2$
Character orbit 2880.bl
Analytic conductor $22.997$
Analytic rank $0$
Dimension $24$
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.bl (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.9969157821\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24q + 8q^{7} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q + 8q^{7} + 24q^{19} + 8q^{37} - 48q^{43} + 24q^{49} - 24q^{55} + 40q^{61} + 40q^{67} + 24q^{85} - 40q^{91} - 16q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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 −4.49261 0 0 0
431.2 0 0 0 −0.707107 − 0.707107i 0 0.750417 0 0 0
431.3 0 0 0 −0.707107 − 0.707107i 0 0.527405 0 0 0
431.4 0 0 0 −0.707107 − 0.707107i 0 −1.61527 0 0 0
431.5 0 0 0 −0.707107 − 0.707107i 0 2.69352 0 0 0
431.6 0 0 0 −0.707107 − 0.707107i 0 4.13654 0 0 0
431.7 0 0 0 0.707107 + 0.707107i 0 −4.49261 0 0 0
431.8 0 0 0 0.707107 + 0.707107i 0 4.13654 0 0 0
431.9 0 0 0 0.707107 + 0.707107i 0 0.527405 0 0 0
431.10 0 0 0 0.707107 + 0.707107i 0 −1.61527 0 0 0
431.11 0 0 0 0.707107 + 0.707107i 0 0.750417 0 0 0
431.12 0 0 0 0.707107 + 0.707107i 0 2.69352 0 0 0
1871.1 0 0 0 −0.707107 + 0.707107i 0 −4.49261 0 0 0
1871.2 0 0 0 −0.707107 + 0.707107i 0 0.750417 0 0 0
1871.3 0 0 0 −0.707107 + 0.707107i 0 0.527405 0 0 0
1871.4 0 0 0 −0.707107 + 0.707107i 0 −1.61527 0 0 0
1871.5 0 0 0 −0.707107 + 0.707107i 0 2.69352 0 0 0
1871.6 0 0 0 −0.707107 + 0.707107i 0 4.13654 0 0 0
1871.7 0 0 0 0.707107 − 0.707107i 0 −4.49261 0 0 0
1871.8 0 0 0 0.707107 − 0.707107i 0 4.13654 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1871.12
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.b 24
3.b odd 2 1 inner 2880.2.bl.b 24
4.b odd 2 1 720.2.bl.b ✓ 24
12.b even 2 1 720.2.bl.b ✓ 24
16.e even 4 1 720.2.bl.b ✓ 24
16.f odd 4 1 inner 2880.2.bl.b 24
48.i odd 4 1 720.2.bl.b ✓ 24
48.k even 4 1 inner 2880.2.bl.b 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
720.2.bl.b ✓ 24 4.b odd 2 1
720.2.bl.b ✓ 24 12.b even 2 1
720.2.bl.b ✓ 24 16.e even 4 1
720.2.bl.b ✓ 24 48.i odd 4 1
2880.2.bl.b 24 1.a even 1 1 trivial
2880.2.bl.b 24 3.b odd 2 1 inner
2880.2.bl.b 24 16.f odd 4 1 inner
2880.2.bl.b 24 48.k even 4 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{6} - 2 T_{7}^{5} - 22 T_{7}^{4} + 48 T_{7}^{3} + 48 T_{7}^{2} - 96 T_{7} + 32 \) acting on \(S_{2}^{\mathrm{new}}(2880, [\chi])\).