# Properties

 Label 4023.2.a.e Level 4023 Weight 2 Character orbit 4023.a Self dual yes Analytic conductor 32.124 Analytic rank 1 Dimension 25 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ = $$4023 = 3^{3} \cdot 149$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4023.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$32.1238167332$$ Analytic rank: $$1$$ Dimension: $$25$$ Coefficient ring index: multiple of None Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$25q - 7q^{2} + 27q^{4} - 12q^{5} - 2q^{7} - 21q^{8} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$25q - 7q^{2} + 27q^{4} - 12q^{5} - 2q^{7} - 21q^{8} - 4q^{10} - 12q^{11} - 10q^{14} + 35q^{16} - 26q^{17} - 30q^{20} + 8q^{22} - 26q^{23} + 27q^{25} - 16q^{26} + 4q^{28} - 20q^{29} - 6q^{31} - 49q^{32} - 14q^{34} - 16q^{35} - 2q^{37} - 27q^{38} + 2q^{40} - 35q^{41} + 4q^{43} - 22q^{44} + 6q^{46} - 38q^{47} + 19q^{49} - 22q^{50} + 4q^{52} - 36q^{53} + 10q^{55} - 79q^{56} - 22q^{58} - 15q^{59} + 10q^{61} + 14q^{62} + 41q^{64} - 80q^{65} - 6q^{67} - 33q^{68} + 8q^{70} - 26q^{71} - 6q^{73} - 75q^{74} - 10q^{76} - 47q^{77} - 6q^{79} - 66q^{80} + 12q^{82} - 40q^{83} - 12q^{85} - 4q^{86} + 12q^{88} - 30q^{89} - 158q^{92} + 18q^{94} - 22q^{95} - 20q^{97} - 35q^{98} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1 −2.82403 0 5.97513 0.305598 0 −1.90246 −11.2259 0 −0.863018
1.2 −2.73865 0 5.50022 −2.48832 0 2.47965 −9.58588 0 6.81463
1.3 −2.51871 0 4.34389 3.54254 0 3.81300 −5.90358 0 −8.92261
1.4 −2.45057 0 4.00528 −3.55507 0 −0.769224 −4.91408 0 8.71195
1.5 −2.18150 0 2.75896 −2.81097 0 0.316017 −1.65567 0 6.13214
1.6 −2.16693 0 2.69559 −1.04157 0 3.90919 −1.50729 0 2.25701
1.7 −1.79652 0 1.22747 3.24604 0 −3.00506 1.38786 0 −5.83156
1.8 −1.51618 0 0.298802 2.07566 0 −1.53996 2.57932 0 −3.14707
1.9 −1.43306 0 0.0536673 −2.81862 0 −4.82450 2.78922 0 4.03925
1.10 −1.23916 0 −0.464485 0.602488 0 1.86008 3.05389 0 −0.746578
1.11 −0.964175 0 −1.07037 0.686967 0 −3.77336 2.96037 0 −0.662356
1.12 −0.614681 0 −1.62217 −3.33074 0 3.77407 2.22648 0 2.04734
1.13 −0.305611 0 −1.90660 1.63568 0 −3.53407 1.19390 0 −0.499884
1.14 −0.0533591 0 −1.99715 0.751347 0 2.49440 0.213285 0 −0.0400912
1.15 0.365778 0 −1.86621 −3.76223 0 −2.92149 −1.41417 0 −1.37614
1.16 0.530451 0 −1.71862 −3.35792 0 3.91494 −1.97255 0 −1.78121
1.17 0.599558 0 −1.64053 0.261228 0 −0.444015 −2.18271 0 0.156622
1.18 0.680129 0 −1.53742 2.78190 0 −0.191226 −2.40591 0 1.89205
1.19 1.30329 0 −0.301424 3.35120 0 −0.705123 −2.99943 0 4.36761
1.20 1.35944 0 −0.151922 −3.36242 0 2.75034 −2.92541 0 −4.57100
See all 25 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.25 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

This newform does not admit any (nontrivial) inner twists.

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4023.2.a.e 25
3.b odd 2 1 4023.2.a.f yes 25

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4023.2.a.e 25 1.a even 1 1 trivial
4023.2.a.f yes 25 3.b odd 2 1

## Atkin-Lehner signs

$$p$$ Sign
$$3$$ $$1$$
$$149$$ $$1$$

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{25} + \cdots$$ acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(4023))$$.