# 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

# 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 $$3$$ and degree $$2$$)

## Newform invariants

 Self dual: No Analytic conductor: $$32.0998616126$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ 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.

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

## 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 −2.18663 + 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: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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 $$S_{2}^{\mathrm{new}}(4020, [\chi])$$:

 $$T_{7}^{24} + \cdots$$ $$T_{11}^{24} + \cdots$$ $$T_{17}^{24} + \cdots$$