Properties

Label 8028.2.h.a
Level 8028
Weight 2
Character orbit 8028.h
Analytic conductor 64.104
Analytic rank 0
Dimension 76
CM No

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Newspace parameters

Level: \( N \) = \( 8028 = 2^{2} \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8028.h (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(64.1039027427\)
Analytic rank: \(0\)
Dimension: \(76\)
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.

\(\operatorname{Tr}(f)(q) = \) \(76q \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(76q \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 100q^{25} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 32q^{37} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 68q^{49} \) \(\mathstrut +\mathstrut 24q^{55} \) \(\mathstrut +\mathstrut 8q^{73} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0 0 0 −4.23105 0 2.43977 0 0 0
4013.2 0 0 0 −4.23105 0 2.43977 0 0 0
4013.3 0 0 0 −3.84036 0 1.75909 0 0 0
4013.4 0 0 0 −3.84036 0 1.75909 0 0 0
4013.5 0 0 0 −3.83180 0 −1.12103 0 0 0
4013.6 0 0 0 −3.83180 0 −1.12103 0 0 0
4013.7 0 0 0 −3.80256 0 0.208948 0 0 0
4013.8 0 0 0 −3.80256 0 0.208948 0 0 0
4013.9 0 0 0 −3.65965 0 −4.62592 0 0 0
4013.10 0 0 0 −3.65965 0 −4.62592 0 0 0
4013.11 0 0 0 −2.81288 0 3.64674 0 0 0
4013.12 0 0 0 −2.81288 0 3.64674 0 0 0
4013.13 0 0 0 −2.68681 0 −3.11614 0 0 0
4013.14 0 0 0 −2.68681 0 −3.11614 0 0 0
4013.15 0 0 0 −2.24499 0 −1.57279 0 0 0
4013.16 0 0 0 −2.24499 0 −1.57279 0 0 0
4013.17 0 0 0 −2.12158 0 2.81365 0 0 0
4013.18 0 0 0 −2.12158 0 2.81365 0 0 0
4013.19 0 0 0 −1.82157 0 −3.59530 0 0 0
4013.20 0 0 0 −1.82157 0 −3.59530 0 0 0
See all 76 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4013.76
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 \(S_{2}^{\mathrm{new}}(8028, [\chi])\).