Properties

Label 4020.2.q.m
Level 4020
Weight 2
Character orbit 4020.q
Analytic conductor 32.100
Analytic rank 0
Dimension 24
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24q + 24q^{3} + 24q^{5} - 3q^{7} + 24q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q + 24q^{3} + 24q^{5} - 3q^{7} + 24q^{9} - 2q^{13} + 24q^{15} - 6q^{19} - 3q^{21} + 2q^{23} + 24q^{25} + 24q^{27} + 7q^{29} - 8q^{31} - 3q^{35} - 10q^{37} - 2q^{39} + 2q^{41} + 28q^{43} + 24q^{45} - 3q^{47} - 17q^{49} + 36q^{53} - 6q^{57} - 10q^{59} + 9q^{61} - 3q^{63} - 2q^{65} - 46q^{67} + 2q^{69} - 12q^{71} + 6q^{73} + 24q^{75} - 5q^{77} + 2q^{79} + 24q^{81} + 11q^{83} + 7q^{87} + 52q^{89} - 22q^{91} - 8q^{93} - 6q^{95} + 3q^{97} + O(q^{100}) \)

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 −2.18663 + 3.78736i 0 1.00000 0
841.2 0 1.00000 0 1.00000 0 −2.09133 + 3.62228i 0 1.00000 0
841.3 0 1.00000 0 1.00000 0 −1.96234 + 3.39887i 0 1.00000 0
841.4 0 1.00000 0 1.00000 0 −1.09486 + 1.89635i 0 1.00000 0
841.5 0 1.00000 0 1.00000 0 −0.436767 + 0.756503i 0 1.00000 0
841.6 0 1.00000 0 1.00000 0 −0.388910 + 0.673613i 0 1.00000 0
841.7 0 1.00000 0 1.00000 0 0.134465 0.232901i 0 1.00000 0
841.8 0 1.00000 0 1.00000 0 0.440752 0.763405i 0 1.00000 0
841.9 0 1.00000 0 1.00000 0 0.983461 1.70340i 0 1.00000 0
841.10 0 1.00000 0 1.00000 0 1.00432 1.73954i 0 1.00000 0
841.11 0 1.00000 0 1.00000 0 1.80478 3.12597i 0 1.00000 0
841.12 0 1.00000 0 1.00000 0 2.29305 3.97167i 0 1.00000 0
3781.1 0 1.00000 0 1.00000 0 −2.18663 3.78736i 0 1.00000 0
3781.2 0 1.00000 0 1.00000 0 −2.09133 3.62228i 0 1.00000 0
3781.3 0 1.00000 0 1.00000 0 −1.96234 3.39887i 0 1.00000 0
3781.4 0 1.00000 0 1.00000 0 −1.09486 1.89635i 0 1.00000 0
3781.5 0 1.00000 0 1.00000 0 −0.436767 0.756503i 0 1.00000 0
3781.6 0 1.00000 0 1.00000 0 −0.388910 0.673613i 0 1.00000 0
3781.7 0 1.00000 0 1.00000 0 0.134465 + 0.232901i 0 1.00000 0
3781.8 0 1.00000 0 1.00000 0 0.440752 + 0.763405i 0 1.00000 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3781.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
67.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4020.2.q.m 24
67.c even 3 1 inner 4020.2.q.m 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4020.2.q.m 24 1.a even 1 1 trivial
4020.2.q.m 24 67.c even 3 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(4020, [\chi])\):

\(T_{7}^{24} + \cdots\)
\(T_{11}^{24} + \cdots\)
\(T_{17}^{24} + \cdots\)