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 Inner twists 2

Related objects

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: $$22$$ Relative dimension: $$11$$ 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.

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

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: Complex embeddings Normalized embeddings Satake parameters Satake angles

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.l 22
67.c even 3 1 inner 4020.2.q.l 22

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4020.2.q.l 22 1.a even 1 1 trivial
4020.2.q.l 22 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 $$S_{2}^{\mathrm{new}}(4020, [\chi])$$:

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