Properties

Label 6048.2.j.d
Level 6048
Weight 2
Character orbit 6048.j
Analytic conductor 48.294
Analytic rank 0
Dimension 48
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.j (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 48q + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 48q - 16q^{19} + 48q^{25} - 64q^{43} - 48q^{49} - 32q^{67} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5615.1 0 0 0 −4.18263 0 1.00000i 0 0 0
5615.2 0 0 0 −4.18263 0 1.00000i 0 0 0
5615.3 0 0 0 −3.69622 0 1.00000i 0 0 0
5615.4 0 0 0 −3.69622 0 1.00000i 0 0 0
5615.5 0 0 0 −2.99711 0 1.00000i 0 0 0
5615.6 0 0 0 −2.99711 0 1.00000i 0 0 0
5615.7 0 0 0 −2.90802 0 1.00000i 0 0 0
5615.8 0 0 0 −2.90802 0 1.00000i 0 0 0
5615.9 0 0 0 −2.85878 0 1.00000i 0 0 0
5615.10 0 0 0 −2.85878 0 1.00000i 0 0 0
5615.11 0 0 0 −2.35025 0 1.00000i 0 0 0
5615.12 0 0 0 −2.35025 0 1.00000i 0 0 0
5615.13 0 0 0 −2.29653 0 1.00000i 0 0 0
5615.14 0 0 0 −2.29653 0 1.00000i 0 0 0
5615.15 0 0 0 −1.27819 0 1.00000i 0 0 0
5615.16 0 0 0 −1.27819 0 1.00000i 0 0 0
5615.17 0 0 0 −1.27600 0 1.00000i 0 0 0
5615.18 0 0 0 −1.27600 0 1.00000i 0 0 0
5615.19 0 0 0 −0.863507 0 1.00000i 0 0 0
5615.20 0 0 0 −0.863507 0 1.00000i 0 0 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5615.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
8.d odd 2 1 inner
24.f even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6048.2.j.d 48
3.b odd 2 1 inner 6048.2.j.d 48
4.b odd 2 1 1512.2.j.d 48
8.b even 2 1 1512.2.j.d 48
8.d odd 2 1 inner 6048.2.j.d 48
12.b even 2 1 1512.2.j.d 48
24.f even 2 1 inner 6048.2.j.d 48
24.h odd 2 1 1512.2.j.d 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1512.2.j.d 48 4.b odd 2 1
1512.2.j.d 48 8.b even 2 1
1512.2.j.d 48 12.b even 2 1
1512.2.j.d 48 24.h odd 2 1
6048.2.j.d 48 1.a even 1 1 trivial
6048.2.j.d 48 3.b odd 2 1 inner
6048.2.j.d 48 8.d odd 2 1 inner
6048.2.j.d 48 24.f even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{5}^{24} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(6048, [\chi])\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database