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

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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 \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.195682095\)
Analytic rank: \(0\)
Dimension: \(48\)
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.

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

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
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

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 \(S_{2}^{\mathrm{new}}(4032, \chi)\):

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