Properties

Label 4020.2.f.a
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.

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

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
401.1 0 −1.73155 0.0417518i 0 −1.00000 0 0.963172i 0 2.99651 + 0.144591i 0
401.2 0 −1.73155 + 0.0417518i 0 −1.00000 0 0.963172i 0 2.99651 0.144591i 0
401.3 0 −1.72437 0.162914i 0 −1.00000 0 4.26819i 0 2.94692 + 0.561849i 0
401.4 0 −1.72437 + 0.162914i 0 −1.00000 0 4.26819i 0 2.94692 0.561849i 0
401.5 0 −1.65289 0.517632i 0 −1.00000 0 0.387683i 0 2.46411 + 1.71118i 0
401.6 0 −1.65289 + 0.517632i 0 −1.00000 0 0.387683i 0 2.46411 1.71118i 0
401.7 0 −1.45039 0.946770i 0 −1.00000 0 1.74006i 0 1.20725 + 2.74637i 0
401.8 0 −1.45039 + 0.946770i 0 −1.00000 0 1.74006i 0 1.20725 2.74637i 0
401.9 0 −1.40436 1.01380i 0 −1.00000 0 3.61166i 0 0.944435 + 2.84746i 0
401.10 0 −1.40436 + 1.01380i 0 −1.00000 0 3.61166i 0 0.944435 2.84746i 0
401.11 0 −1.30028 1.14423i 0 −1.00000 0 3.38238i 0 0.381467 + 2.97565i 0
401.12 0 −1.30028 + 1.14423i 0 −1.00000 0 3.38238i 0 0.381467 2.97565i 0
401.13 0 −1.15074 1.29452i 0 −1.00000 0 2.00748i 0 −0.351574 + 2.97933i 0
401.14 0 −1.15074 + 1.29452i 0 −1.00000 0 2.00748i 0 −0.351574 2.97933i 0
401.15 0 −0.963300 1.43946i 0 −1.00000 0 2.54461i 0 −1.14411 + 2.77327i 0
401.16 0 −0.963300 + 1.43946i 0 −1.00000 0 2.54461i 0 −1.14411 2.77327i 0
401.17 0 −0.574646 1.63395i 0 −1.00000 0 4.28520i 0 −2.33956 + 1.87788i 0
401.18 0 −0.574646 + 1.63395i 0 −1.00000 0 4.28520i 0 −2.33956 1.87788i 0
401.19 0 −0.370384 1.69199i 0 −1.00000 0 0.0825586i 0 −2.72563 + 1.25337i 0
401.20 0 −0.370384 + 1.69199i 0 −1.00000 0 0.0825586i 0 −2.72563 1.25337i 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.