Properties

Label 6048.2.c.g
Level 6048
Weight 2
Character orbit 6048.c
Analytic conductor 48.294
Analytic rank 0
Dimension 24
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.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24q - 24q^{7} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q - 24q^{7} - 24q^{25} + 16q^{31} + 24q^{49} + 8q^{55} - 32q^{79} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3025.1 0 0 0 3.66698i 0 −1.00000 0 0 0
3025.2 0 0 0 3.66698i 0 −1.00000 0 0 0
3025.3 0 0 0 3.11390i 0 −1.00000 0 0 0
3025.4 0 0 0 3.11390i 0 −1.00000 0 0 0
3025.5 0 0 0 2.52623i 0 −1.00000 0 0 0
3025.6 0 0 0 2.52623i 0 −1.00000 0 0 0
3025.7 0 0 0 1.58470i 0 −1.00000 0 0 0
3025.8 0 0 0 1.58470i 0 −1.00000 0 0 0
3025.9 0 0 0 1.53368i 0 −1.00000 0 0 0
3025.10 0 0 0 1.53368i 0 −1.00000 0 0 0
3025.11 0 0 0 1.26947i 0 −1.00000 0 0 0
3025.12 0 0 0 1.26947i 0 −1.00000 0 0 0
3025.13 0 0 0 1.26947i 0 −1.00000 0 0 0
3025.14 0 0 0 1.26947i 0 −1.00000 0 0 0
3025.15 0 0 0 1.53368i 0 −1.00000 0 0 0
3025.16 0 0 0 1.53368i 0 −1.00000 0 0 0
3025.17 0 0 0 1.58470i 0 −1.00000 0 0 0
3025.18 0 0 0 1.58470i 0 −1.00000 0 0 0
3025.19 0 0 0 2.52623i 0 −1.00000 0 0 0
3025.20 0 0 0 2.52623i 0 −1.00000 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3025.24
Significant digits:
Format:

Inner twists

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

Twists

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(6048, [\chi])\):

\( T_{5}^{12} + 36 T_{5}^{10} + 483 T_{5}^{8} + 3048 T_{5}^{6} + 9491 T_{5}^{4} + 14084 T_{5}^{2} + 7921 \)
\( T_{17}^{12} - 124 T_{17}^{10} + 5788 T_{17}^{8} - 128800 T_{17}^{6} + 1407472 T_{17}^{4} - 6700992 T_{17}^{2} + 8156736 \)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database