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

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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 \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(32.195682095\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
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.

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

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:
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Inner twists

This newform does not have CM; other inner twists have not been computed.

Hecke kernels

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

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