Properties

Label 4032.2.i.c
Level 4032
Weight 2
Character orbit 4032.i
Analytic conductor 32.196
Analytic rank 0
Dimension 48
CM no
Inner twists 16

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Newspace parameters

Level: \( N \) \(=\) \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4032.i (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.1956820950\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 48q + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 48q - 80q^{25} - 16q^{49} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1889.1 0 0 0 1.77767i 0 −2.39248 1.12962i 0 0 0
1889.2 0 0 0 1.77767i 0 −2.39248 + 1.12962i 0 0 0
1889.3 0 0 0 1.21807i 0 0.355387 2.62177i 0 0 0
1889.4 0 0 0 1.21807i 0 0.355387 + 2.62177i 0 0 0
1889.5 0 0 0 1.77767i 0 −2.39248 1.12962i 0 0 0
1889.6 0 0 0 1.77767i 0 −2.39248 + 1.12962i 0 0 0
1889.7 0 0 0 3.91870i 0 2.03709 1.68827i 0 0 0
1889.8 0 0 0 3.91870i 0 2.03709 + 1.68827i 0 0 0
1889.9 0 0 0 1.21807i 0 0.355387 + 2.62177i 0 0 0
1889.10 0 0 0 1.21807i 0 0.355387 2.62177i 0 0 0
1889.11 0 0 0 1.77767i 0 2.39248 1.12962i 0 0 0
1889.12 0 0 0 1.77767i 0 2.39248 + 1.12962i 0 0 0
1889.13 0 0 0 3.91870i 0 2.03709 1.68827i 0 0 0
1889.14 0 0 0 3.91870i 0 2.03709 + 1.68827i 0 0 0
1889.15 0 0 0 3.91870i 0 2.03709 + 1.68827i 0 0 0
1889.16 0 0 0 3.91870i 0 2.03709 1.68827i 0 0 0
1889.17 0 0 0 3.91870i 0 −2.03709 1.68827i 0 0 0
1889.18 0 0 0 3.91870i 0 −2.03709 + 1.68827i 0 0 0
1889.19 0 0 0 1.77767i 0 −2.39248 + 1.12962i 0 0 0
1889.20 0 0 0 1.77767i 0 −2.39248 1.12962i 0 0 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1889.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
4.b odd 2 1 inner
7.b odd 2 1 inner
8.b even 2 1 inner
8.d odd 2 1 inner
12.b even 2 1 inner
21.c even 2 1 inner
24.f even 2 1 inner
24.h odd 2 1 inner
28.d even 2 1 inner
56.e even 2 1 inner
56.h odd 2 1 inner
84.h odd 2 1 inner
168.e odd 2 1 inner
168.i even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4032.2.i.c 48
3.b odd 2 1 inner 4032.2.i.c 48
4.b odd 2 1 inner 4032.2.i.c 48
7.b odd 2 1 inner 4032.2.i.c 48
8.b even 2 1 inner 4032.2.i.c 48
8.d odd 2 1 inner 4032.2.i.c 48
12.b even 2 1 inner 4032.2.i.c 48
21.c even 2 1 inner 4032.2.i.c 48
24.f even 2 1 inner 4032.2.i.c 48
24.h odd 2 1 inner 4032.2.i.c 48
28.d even 2 1 inner 4032.2.i.c 48
56.e even 2 1 inner 4032.2.i.c 48
56.h odd 2 1 inner 4032.2.i.c 48
84.h odd 2 1 inner 4032.2.i.c 48
168.e odd 2 1 inner 4032.2.i.c 48
168.i even 2 1 inner 4032.2.i.c 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4032.2.i.c 48 1.a even 1 1 trivial
4032.2.i.c 48 3.b odd 2 1 inner
4032.2.i.c 48 4.b odd 2 1 inner
4032.2.i.c 48 7.b odd 2 1 inner
4032.2.i.c 48 8.b even 2 1 inner
4032.2.i.c 48 8.d odd 2 1 inner
4032.2.i.c 48 12.b even 2 1 inner
4032.2.i.c 48 21.c even 2 1 inner
4032.2.i.c 48 24.f even 2 1 inner
4032.2.i.c 48 24.h odd 2 1 inner
4032.2.i.c 48 28.d even 2 1 inner
4032.2.i.c 48 56.e even 2 1 inner
4032.2.i.c 48 56.h odd 2 1 inner
4032.2.i.c 48 84.h odd 2 1 inner
4032.2.i.c 48 168.e odd 2 1 inner
4032.2.i.c 48 168.i even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(4032, [\chi])\):

\( T_{5}^{6} + 20 T_{5}^{4} + 76 T_{5}^{2} + 72 \)
\( T_{47}^{6} - 128 T_{47}^{4} + 3520 T_{47}^{2} - 4608 \)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database