Properties

Label 4020.2.f.b
Level 4020
Weight 2
Character orbit 4020.f
Analytic conductor 32.100
Analytic rank 0
Dimension 46
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.f (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(46\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 46q + 46q^{5} - 4q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 46q + 46q^{5} - 4q^{9} + 8q^{19} + 46q^{25} + 18q^{27} + 4q^{33} - 8q^{37} - 12q^{39} + 4q^{41} - 4q^{45} - 62q^{49} + 8q^{51} + 8q^{53} + 12q^{57} + 10q^{63} - 14q^{67} - 40q^{73} - 12q^{81} - 4q^{91} + 2q^{93} + 8q^{95} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
401.1 0 −1.70172 0.322705i 0 1.00000 0 1.22892i 0 2.79172 + 1.09831i 0
401.2 0 −1.70172 + 0.322705i 0 1.00000 0 1.22892i 0 2.79172 1.09831i 0
401.3 0 −1.68102 0.417348i 0 1.00000 0 2.42754i 0 2.65164 + 1.40314i 0
401.4 0 −1.68102 + 0.417348i 0 1.00000 0 2.42754i 0 2.65164 1.40314i 0
401.5 0 −1.65640 0.506295i 0 1.00000 0 4.66467i 0 2.48733 + 1.67726i 0
401.6 0 −1.65640 + 0.506295i 0 1.00000 0 4.66467i 0 2.48733 1.67726i 0
401.7 0 −1.37038 1.05928i 0 1.00000 0 0.226959i 0 0.755857 + 2.90322i 0
401.8 0 −1.37038 + 1.05928i 0 1.00000 0 0.226959i 0 0.755857 2.90322i 0
401.9 0 −1.24570 1.20343i 0 1.00000 0 4.23048i 0 0.103517 + 2.99821i 0
401.10 0 −1.24570 + 1.20343i 0 1.00000 0 4.23048i 0 0.103517 2.99821i 0
401.11 0 −1.14102 1.30310i 0 1.00000 0 5.02322i 0 −0.396144 + 2.97373i 0
401.12 0 −1.14102 + 1.30310i 0 1.00000 0 5.02322i 0 −0.396144 2.97373i 0
401.13 0 −1.10897 1.33049i 0 1.00000 0 2.36440i 0 −0.540386 + 2.95093i 0
401.14 0 −1.10897 + 1.33049i 0 1.00000 0 2.36440i 0 −0.540386 2.95093i 0
401.15 0 −1.06681 1.36452i 0 1.00000 0 1.51153i 0 −0.723813 + 2.91137i 0
401.16 0 −1.06681 + 1.36452i 0 1.00000 0 1.51153i 0 −0.723813 2.91137i 0
401.17 0 −0.747634 1.56238i 0 1.00000 0 2.57301i 0 −1.88209 + 2.33618i 0
401.18 0 −0.747634 + 1.56238i 0 1.00000 0 2.57301i 0 −1.88209 2.33618i 0
401.19 0 −0.296734 1.70644i 0 1.00000 0 4.76000i 0 −2.82390 + 1.01272i 0
401.20 0 −0.296734 + 1.70644i 0 1.00000 0 4.76000i 0 −2.82390 1.01272i 0
See all 46 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 401.46
Significant digits:
Format:

Inner twists

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