Properties

Label 4032.2.v.d
Level 4032
Weight 2
Character orbit 4032.v
Analytic conductor 32.196
Analytic rank 0
Dimension 36
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: \(36\)
Relative dimension: \(18\) 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.

\(\operatorname{Tr}(f)(q) = \) \(36q \) \(\mathstrut +\mathstrut 36q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(36q \) \(\mathstrut +\mathstrut 36q^{7} \) \(\mathstrut -\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 36q^{43} \) \(\mathstrut +\mathstrut 36q^{49} \) \(\mathstrut -\mathstrut 32q^{55} \) \(\mathstrut +\mathstrut 112q^{61} \) \(\mathstrut +\mathstrut 36q^{67} \) \(\mathstrut -\mathstrut 96q^{85} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 56q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.98923 2.98923i 0 1.00000 0 0 0
1583.2 0 0 0 −2.53823 2.53823i 0 1.00000 0 0 0
1583.3 0 0 0 −2.28967 2.28967i 0 1.00000 0 0 0
1583.4 0 0 0 −2.01396 2.01396i 0 1.00000 0 0 0
1583.5 0 0 0 −1.68827 1.68827i 0 1.00000 0 0 0
1583.6 0 0 0 −1.18126 1.18126i 0 1.00000 0 0 0
1583.7 0 0 0 −0.871498 0.871498i 0 1.00000 0 0 0
1583.8 0 0 0 −0.495166 0.495166i 0 1.00000 0 0 0
1583.9 0 0 0 −0.270063 0.270063i 0 1.00000 0 0 0
1583.10 0 0 0 0.270063 + 0.270063i 0 1.00000 0 0 0
1583.11 0 0 0 0.495166 + 0.495166i 0 1.00000 0 0 0
1583.12 0 0 0 0.871498 + 0.871498i 0 1.00000 0 0 0
1583.13 0 0 0 1.18126 + 1.18126i 0 1.00000 0 0 0
1583.14 0 0 0 1.68827 + 1.68827i 0 1.00000 0 0 0
1583.15 0 0 0 2.01396 + 2.01396i 0 1.00000 0 0 0
1583.16 0 0 0 2.28967 + 2.28967i 0 1.00000 0 0 0
1583.17 0 0 0 2.53823 + 2.53823i 0 1.00000 0 0 0
1583.18 0 0 0 2.98923 + 2.98923i 0 1.00000 0 0 0
3599.1 0 0 0 −2.98923 + 2.98923i 0 1.00000 0 0 0
3599.2 0 0 0 −2.53823 + 2.53823i 0 1.00000 0 0 0
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3599.18
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 \(S_{2}^{\mathrm{new}}(4032, [\chi])\):

\(T_{5}^{36} + \cdots\)
\(T_{11}^{36} + \cdots\)