Properties

Label 4032.2.v.e
Level 4032
Weight 2
Character orbit 4032.v
Analytic conductor 32.196
Analytic rank 0
Dimension 40
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.v (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.1956820950\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 1008)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40q - 40q^{7} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 40q - 40q^{7} - 24q^{13} + 32q^{19} - 8q^{37} - 32q^{43} + 40q^{49} - 48q^{55} - 24q^{61} + 64q^{85} + 24q^{91} + 64q^{97} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1583.1 0 0 0 −2.96859 2.96859i 0 −1.00000 0 0 0
1583.2 0 0 0 −2.62814 2.62814i 0 −1.00000 0 0 0
1583.3 0 0 0 −2.51504 2.51504i 0 −1.00000 0 0 0
1583.4 0 0 0 −2.12043 2.12043i 0 −1.00000 0 0 0
1583.5 0 0 0 −1.65702 1.65702i 0 −1.00000 0 0 0
1583.6 0 0 0 −1.17902 1.17902i 0 −1.00000 0 0 0
1583.7 0 0 0 −0.925496 0.925496i 0 −1.00000 0 0 0
1583.8 0 0 0 −0.667815 0.667815i 0 −1.00000 0 0 0
1583.9 0 0 0 −0.111394 0.111394i 0 −1.00000 0 0 0
1583.10 0 0 0 −0.0893433 0.0893433i 0 −1.00000 0 0 0
1583.11 0 0 0 0.0893433 + 0.0893433i 0 −1.00000 0 0 0
1583.12 0 0 0 0.111394 + 0.111394i 0 −1.00000 0 0 0
1583.13 0 0 0 0.667815 + 0.667815i 0 −1.00000 0 0 0
1583.14 0 0 0 0.925496 + 0.925496i 0 −1.00000 0 0 0
1583.15 0 0 0 1.17902 + 1.17902i 0 −1.00000 0 0 0
1583.16 0 0 0 1.65702 + 1.65702i 0 −1.00000 0 0 0
1583.17 0 0 0 2.12043 + 2.12043i 0 −1.00000 0 0 0
1583.18 0 0 0 2.51504 + 2.51504i 0 −1.00000 0 0 0
1583.19 0 0 0 2.62814 + 2.62814i 0 −1.00000 0 0 0
1583.20 0 0 0 2.96859 + 2.96859i 0 −1.00000 0 0 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3599.20
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 4032.2.v.e 40
3.b odd 2 1 inner 4032.2.v.e 40
4.b odd 2 1 1008.2.v.e 40
12.b even 2 1 1008.2.v.e 40
16.e even 4 1 1008.2.v.e 40
16.f odd 4 1 inner 4032.2.v.e 40
48.i odd 4 1 1008.2.v.e 40
48.k even 4 1 inner 4032.2.v.e 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1008.2.v.e 40 4.b odd 2 1
1008.2.v.e 40 12.b even 2 1
1008.2.v.e 40 16.e even 4 1
1008.2.v.e 40 48.i odd 4 1
4032.2.v.e 40 1.a even 1 1 trivial
4032.2.v.e 40 3.b odd 2 1 inner
4032.2.v.e 40 16.f odd 4 1 inner
4032.2.v.e 40 48.k even 4 1 inner

Hecke kernels

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

\(T_{5}^{40} + \cdots\)
\(T_{11}^{40} + \cdots\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database