Properties

Label 4020.2.g.c
Level 4020
Weight 2
Character orbit 4020.g
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(38\)
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.

\(\operatorname{Tr}(f)(q) = \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1609.1 0 1.00000i 0 −2.23543 + 0.0533841i 0 4.50874i 0 −1.00000 0
1609.2 0 1.00000i 0 −2.22744 + 0.196195i 0 0.128273i 0 −1.00000 0
1609.3 0 1.00000i 0 −2.06455 + 0.858848i 0 3.58783i 0 −1.00000 0
1609.4 0 1.00000i 0 −2.02556 0.947153i 0 2.95752i 0 −1.00000 0
1609.5 0 1.00000i 0 −1.48830 + 1.66882i 0 2.27974i 0 −1.00000 0
1609.6 0 1.00000i 0 −0.953985 2.02235i 0 5.11769i 0 −1.00000 0
1609.7 0 1.00000i 0 −0.847850 + 2.06909i 0 3.67313i 0 −1.00000 0
1609.8 0 1.00000i 0 −0.676225 2.13137i 0 4.23231i 0 −1.00000 0
1609.9 0 1.00000i 0 −0.599682 2.15415i 0 0.0778518i 0 −1.00000 0
1609.10 0 1.00000i 0 −0.504884 2.17832i 0 3.91807i 0 −1.00000 0
1609.11 0 1.00000i 0 −0.471887 + 2.18571i 0 1.05400i 0 −1.00000 0
1609.12 0 1.00000i 0 0.145309 + 2.23134i 0 1.12842i 0 −1.00000 0
1609.13 0 1.00000i 0 1.17292 1.90375i 0 2.37828i 0 −1.00000 0
1609.14 0 1.00000i 0 1.34274 + 1.78803i 0 0.521655i 0 −1.00000 0
1609.15 0 1.00000i 0 1.96436 + 1.06831i 0 3.03191i 0 −1.00000 0
1609.16 0 1.00000i 0 1.96624 + 1.06486i 0 4.32230i 0 −1.00000 0
1609.17 0 1.00000i 0 2.08125 0.817560i 0 3.41849i 0 −1.00000 0
1609.18 0 1.00000i 0 2.20926 0.345224i 0 0.0620642i 0 −1.00000 0
1609.19 0 1.00000i 0 2.21373 + 0.315287i 0 0.0918930i 0 −1.00000 0
1609.20 0 1.00000i 0 −2.23543 0.0533841i 0 4.50874i 0 −1.00000 0
See all 38 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1609.38
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 kernel of the linear operator \(T_{7}^{38} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(4020, [\chi])\).