Properties

Label 4014.2.d.a
Level 4014
Weight 2
Character orbit 4014.d
Analytic conductor 32.052
Analytic rank 0
Dimension 72
CM No

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Newspace parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0519513713\)
Analytic rank: \(0\)
Dimension: \(72\)
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.

\(\operatorname{Tr}(f)(q) = \) \(72q \) \(\mathstrut -\mathstrut 72q^{4} \) \(\mathstrut +\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(72q \) \(\mathstrut -\mathstrut 72q^{4} \) \(\mathstrut +\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut 72q^{16} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 96q^{25} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut -\mathstrut 24q^{37} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 56q^{49} \) \(\mathstrut +\mathstrut 40q^{58} \) \(\mathstrut -\mathstrut 72q^{64} \) \(\mathstrut -\mathstrut 32q^{73} \) \(\mathstrut +\mathstrut 40q^{76} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4013.1 1.00000i 0 −1.00000 3.51050 0 3.72470 1.00000i 0 3.51050i
4013.2 1.00000i 0 −1.00000 3.51050 0 3.72470 1.00000i 0 3.51050i
4013.3 1.00000i 0 −1.00000 −0.969046 0 −3.46872 1.00000i 0 0.969046i
4013.4 1.00000i 0 −1.00000 −0.969046 0 −3.46872 1.00000i 0 0.969046i
4013.5 1.00000i 0 −1.00000 −2.31709 0 −2.47546 1.00000i 0 2.31709i
4013.6 1.00000i 0 −1.00000 −2.31709 0 −2.47546 1.00000i 0 2.31709i
4013.7 1.00000i 0 −1.00000 0.125404 0 3.10184 1.00000i 0 0.125404i
4013.8 1.00000i 0 −1.00000 0.125404 0 3.10184 1.00000i 0 0.125404i
4013.9 1.00000i 0 −1.00000 3.59603 0 4.66381 1.00000i 0 3.59603i
4013.10 1.00000i 0 −1.00000 3.59603 0 4.66381 1.00000i 0 3.59603i
4013.11 1.00000i 0 −1.00000 −2.58876 0 −1.62417 1.00000i 0 2.58876i
4013.12 1.00000i 0 −1.00000 −2.58876 0 −1.62417 1.00000i 0 2.58876i
4013.13 1.00000i 0 −1.00000 2.29842 0 2.05558 1.00000i 0 2.29842i
4013.14 1.00000i 0 −1.00000 2.29842 0 2.05558 1.00000i 0 2.29842i
4013.15 1.00000i 0 −1.00000 −2.37383 0 3.81286 1.00000i 0 2.37383i
4013.16 1.00000i 0 −1.00000 −2.37383 0 3.81286 1.00000i 0 2.37383i
4013.17 1.00000i 0 −1.00000 0.707934 0 0.916361 1.00000i 0 0.707934i
4013.18 1.00000i 0 −1.00000 0.707934 0 0.916361 1.00000i 0 0.707934i
4013.19 1.00000i 0 −1.00000 −1.71459 0 2.72316 1.00000i 0 1.71459i
4013.20 1.00000i 0 −1.00000 −1.71459 0 2.72316 1.00000i 0 1.71459i
See all 72 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4013.72
Significant digits:
Format:

Inner twists

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

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(4014, \chi)\).