Properties

Label 4028.2.c.a
Level 4028
Weight 2
Character orbit 4028.c
Analytic conductor 32.164
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.1637419342\)
Analytic rank: \(0\)
Dimension: \(82\)
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.

\(\operatorname{Tr}(f)(q) = \) \(82q \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 82q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(82q \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 82q^{9} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 98q^{49} \) \(\mathstrut +\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 28q^{69} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 154q^{81} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut -\mathstrut 56q^{93} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3497.1 0 3.43171i 0 2.90667i 0 −0.616337 0 −8.77663 0
3497.2 0 3.32000i 0 0.481923i 0 4.89204 0 −8.02243 0
3497.3 0 3.26219i 0 2.63587i 0 −3.36239 0 −7.64188 0
3497.4 0 3.23093i 0 3.15613i 0 −4.75851 0 −7.43889 0
3497.5 0 3.07917i 0 0.328536i 0 −0.0673750 0 −6.48127 0
3497.6 0 3.02294i 0 2.23488i 0 1.30562 0 −6.13814 0
3497.7 0 2.92218i 0 2.97792i 0 2.58698 0 −5.53915 0
3497.8 0 2.85178i 0 0.944719i 0 0.420631 0 −5.13267 0
3497.9 0 2.65407i 0 1.30709i 0 −2.08185 0 −4.04406 0
3497.10 0 2.57074i 0 2.44297i 0 3.60312 0 −3.60868 0
3497.11 0 2.47054i 0 0.894697i 0 −2.25054 0 −3.10359 0
3497.12 0 2.46723i 0 4.35102i 0 1.12403 0 −3.08725 0
3497.13 0 2.38052i 0 1.77530i 0 −1.28291 0 −2.66687 0
3497.14 0 2.33396i 0 3.41794i 0 2.47388 0 −2.44737 0
3497.15 0 2.31112i 0 0.310021i 0 2.57819 0 −2.34128 0
3497.16 0 2.26231i 0 0.110491i 0 −4.79793 0 −2.11803 0
3497.17 0 2.19213i 0 3.88947i 0 −3.90251 0 −1.80545 0
3497.18 0 2.07591i 0 1.80942i 0 1.11331 0 −1.30941 0
3497.19 0 2.06657i 0 3.50814i 0 2.22099 0 −1.27069 0
3497.20 0 1.77695i 0 3.36332i 0 −1.55852 0 −0.157556 0
See all 82 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3497.82
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 \(S_{2}^{\mathrm{new}}(4028, \chi)\).