Properties

Label 4020.2.q.l
Level 4020
Weight 2
Character orbit 4020.q
Analytic conductor 32.100
Analytic rank 0
Dimension 22
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.q (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \(22q \) \(\mathstrut -\mathstrut 22q^{3} \) \(\mathstrut -\mathstrut 22q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut 22q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(22q \) \(\mathstrut -\mathstrut 22q^{3} \) \(\mathstrut -\mathstrut 22q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut 22q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 22q^{15} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut -\mathstrut 22q^{27} \) \(\mathstrut +\mathstrut 15q^{29} \) \(\mathstrut -\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut q^{35} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 22q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 16q^{49} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut +\mathstrut 8q^{61} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 7q^{65} \) \(\mathstrut -\mathstrut 9q^{67} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut q^{73} \) \(\mathstrut -\mathstrut 22q^{75} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 22q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut +\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 18q^{91} \) \(\mathstrut +\mathstrut 5q^{93} \) \(\mathstrut -\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 16q^{97} \) \(\mathstrut -\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
841.1 0 −1.00000 0 −1.00000 0 −2.18326 + 3.78152i 0 1.00000 0
841.2 0 −1.00000 0 −1.00000 0 −1.77038 + 3.06640i 0 1.00000 0
841.3 0 −1.00000 0 −1.00000 0 −1.49766 + 2.59403i 0 1.00000 0
841.4 0 −1.00000 0 −1.00000 0 −0.775137 + 1.34258i 0 1.00000 0
841.5 0 −1.00000 0 −1.00000 0 −0.533315 + 0.923729i 0 1.00000 0
841.6 0 −1.00000 0 −1.00000 0 0.278615 0.482575i 0 1.00000 0
841.7 0 −1.00000 0 −1.00000 0 0.479055 0.829747i 0 1.00000 0
841.8 0 −1.00000 0 −1.00000 0 0.637931 1.10493i 0 1.00000 0
841.9 0 −1.00000 0 −1.00000 0 1.82121 3.15443i 0 1.00000 0
841.10 0 −1.00000 0 −1.00000 0 1.92862 3.34047i 0 1.00000 0
841.11 0 −1.00000 0 −1.00000 0 2.11433 3.66213i 0 1.00000 0
3781.1 0 −1.00000 0 −1.00000 0 −2.18326 3.78152i 0 1.00000 0
3781.2 0 −1.00000 0 −1.00000 0 −1.77038 3.06640i 0 1.00000 0
3781.3 0 −1.00000 0 −1.00000 0 −1.49766 2.59403i 0 1.00000 0
3781.4 0 −1.00000 0 −1.00000 0 −0.775137 1.34258i 0 1.00000 0
3781.5 0 −1.00000 0 −1.00000 0 −0.533315 0.923729i 0 1.00000 0
3781.6 0 −1.00000 0 −1.00000 0 0.278615 + 0.482575i 0 1.00000 0
3781.7 0 −1.00000 0 −1.00000 0 0.479055 + 0.829747i 0 1.00000 0
3781.8 0 −1.00000 0 −1.00000 0 0.637931 + 1.10493i 0 1.00000 0
3781.9 0 −1.00000 0 −1.00000 0 1.82121 + 3.15443i 0 1.00000 0
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3781.11
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 intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(4020, \chi)\):

\(T_{7}^{22} - \cdots\)
\(T_{11}^{22} + \cdots\)
\(T_{17}^{22} - \cdots\)