# Properties

 Label 4020.2.g.b Level 4020 Weight 2 Character orbit 4020.g Analytic conductor 32.100 Analytic rank 0 Dimension 24 CM No

# Related objects

## Newspace parameters

 Level: $$N$$ = $$4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4020.g (of order $$2$$ and degree $$1$$)

## Newform invariants

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

 $$\operatorname{Tr}(f)(q) =$$ $$24q$$ $$\mathstrut -\mathstrut 4q^{5}$$ $$\mathstrut -\mathstrut 24q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q$$ $$\mathstrut -\mathstrut 4q^{5}$$ $$\mathstrut -\mathstrut 24q^{9}$$ $$\mathstrut -\mathstrut 8q^{11}$$ $$\mathstrut -\mathstrut 2q^{15}$$ $$\mathstrut +\mathstrut 16q^{19}$$ $$\mathstrut -\mathstrut 20q^{21}$$ $$\mathstrut +\mathstrut 10q^{25}$$ $$\mathstrut +\mathstrut 36q^{29}$$ $$\mathstrut -\mathstrut 2q^{35}$$ $$\mathstrut +\mathstrut 4q^{39}$$ $$\mathstrut -\mathstrut 24q^{41}$$ $$\mathstrut +\mathstrut 4q^{45}$$ $$\mathstrut -\mathstrut 4q^{51}$$ $$\mathstrut -\mathstrut 4q^{55}$$ $$\mathstrut +\mathstrut 24q^{59}$$ $$\mathstrut -\mathstrut 4q^{61}$$ $$\mathstrut -\mathstrut 20q^{65}$$ $$\mathstrut -\mathstrut 4q^{69}$$ $$\mathstrut +\mathstrut 20q^{71}$$ $$\mathstrut -\mathstrut 12q^{75}$$ $$\mathstrut -\mathstrut 28q^{79}$$ $$\mathstrut +\mathstrut 24q^{81}$$ $$\mathstrut -\mathstrut 16q^{85}$$ $$\mathstrut +\mathstrut 48q^{89}$$ $$\mathstrut -\mathstrut 20q^{91}$$ $$\mathstrut -\mathstrut 4q^{95}$$ $$\mathstrut +\mathstrut 8q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1609.1 0 1.00000i 0 −2.22339 0.237781i 0 1.39060i 0 −1.00000 0
1609.2 0 1.00000i 0 −2.07549 0.832066i 0 0.944795i 0 −1.00000 0
1609.3 0 1.00000i 0 −1.71974 1.42915i 0 1.37984i 0 −1.00000 0
1609.4 0 1.00000i 0 −1.63494 + 1.52544i 0 3.48382i 0 −1.00000 0
1609.5 0 1.00000i 0 −1.47707 + 1.67877i 0 3.23400i 0 −1.00000 0
1609.6 0 1.00000i 0 −0.880059 2.05560i 0 1.30492i 0 −1.00000 0
1609.7 0 1.00000i 0 −0.131247 + 2.23221i 0 5.13753i 0 −1.00000 0
1609.8 0 1.00000i 0 0.853331 + 2.06684i 0 2.56410i 0 −1.00000 0
1609.9 0 1.00000i 0 1.39369 1.74860i 0 3.23145i 0 −1.00000 0
1609.10 0 1.00000i 0 1.45456 1.69831i 0 0.243187i 0 −1.00000 0
1609.11 0 1.00000i 0 2.21022 0.339036i 0 3.30262i 0 −1.00000 0
1609.12 0 1.00000i 0 2.23014 0.162710i 0 0.770377i 0 −1.00000 0
1609.13 0 1.00000i 0 −2.22339 + 0.237781i 0 1.39060i 0 −1.00000 0
1609.14 0 1.00000i 0 −2.07549 + 0.832066i 0 0.944795i 0 −1.00000 0
1609.15 0 1.00000i 0 −1.71974 + 1.42915i 0 1.37984i 0 −1.00000 0
1609.16 0 1.00000i 0 −1.63494 1.52544i 0 3.48382i 0 −1.00000 0
1609.17 0 1.00000i 0 −1.47707 1.67877i 0 3.23400i 0 −1.00000 0
1609.18 0 1.00000i 0 −0.880059 + 2.05560i 0 1.30492i 0 −1.00000 0
1609.19 0 1.00000i 0 −0.131247 2.23221i 0 5.13753i 0 −1.00000 0
1609.20 0 1.00000i 0 0.853331 2.06684i 0 2.56410i 0 −1.00000 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1609.24 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 kernel of the linear operator $$T_{7}^{24} + \cdots$$ acting on $$S_{2}^{\mathrm{new}}(4020, \chi)$$.