Properties

 Label 5733.2.a.e Level $5733$ Weight $2$ Character orbit 5733.a Self dual yes Analytic conductor $45.778$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$5733 = 3^{2} \cdot 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5733.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$45.7782354788$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 39) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} - q^{4} + 2 q^{5} + 3 q^{8}+O(q^{10})$$ q - q^2 - q^4 + 2 * q^5 + 3 * q^8 $$q - q^{2} - q^{4} + 2 q^{5} + 3 q^{8} - 2 q^{10} - 4 q^{11} - q^{13} - q^{16} + 2 q^{17} - 2 q^{20} + 4 q^{22} - q^{25} + q^{26} + 10 q^{29} - 4 q^{31} - 5 q^{32} - 2 q^{34} - 2 q^{37} + 6 q^{40} + 6 q^{41} - 12 q^{43} + 4 q^{44} + q^{50} + q^{52} - 6 q^{53} - 8 q^{55} - 10 q^{58} + 12 q^{59} + 2 q^{61} + 4 q^{62} + 7 q^{64} - 2 q^{65} - 8 q^{67} - 2 q^{68} - 2 q^{73} + 2 q^{74} + 8 q^{79} - 2 q^{80} - 6 q^{82} + 4 q^{83} + 4 q^{85} + 12 q^{86} - 12 q^{88} - 2 q^{89} - 10 q^{97}+O(q^{100})$$ q - q^2 - q^4 + 2 * q^5 + 3 * q^8 - 2 * q^10 - 4 * q^11 - q^13 - q^16 + 2 * q^17 - 2 * q^20 + 4 * q^22 - q^25 + q^26 + 10 * q^29 - 4 * q^31 - 5 * q^32 - 2 * q^34 - 2 * q^37 + 6 * q^40 + 6 * q^41 - 12 * q^43 + 4 * q^44 + q^50 + q^52 - 6 * q^53 - 8 * q^55 - 10 * q^58 + 12 * q^59 + 2 * q^61 + 4 * q^62 + 7 * q^64 - 2 * q^65 - 8 * q^67 - 2 * q^68 - 2 * q^73 + 2 * q^74 + 8 * q^79 - 2 * q^80 - 6 * q^82 + 4 * q^83 + 4 * q^85 + 12 * q^86 - 12 * q^88 - 2 * q^89 - 10 * q^97

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 $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
 0
−1.00000 0 −1.00000 2.00000 0 0 3.00000 0 −2.00000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

$$p$$ Sign
$$3$$ $$-1$$
$$7$$ $$-1$$
$$13$$ $$1$$

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 5733.2.a.e 1
3.b odd 2 1 1911.2.a.f 1
7.b odd 2 1 117.2.a.a 1
21.c even 2 1 39.2.a.a 1
28.d even 2 1 1872.2.a.h 1
35.c odd 2 1 2925.2.a.p 1
35.f even 4 2 2925.2.c.e 2
56.e even 2 1 7488.2.a.by 1
56.h odd 2 1 7488.2.a.bl 1
63.l odd 6 2 1053.2.e.d 2
63.o even 6 2 1053.2.e.b 2
84.h odd 2 1 624.2.a.i 1
91.b odd 2 1 1521.2.a.e 1
91.i even 4 2 1521.2.b.b 2
105.g even 2 1 975.2.a.f 1
105.k odd 4 2 975.2.c.f 2
168.e odd 2 1 2496.2.a.e 1
168.i even 2 1 2496.2.a.q 1
231.h odd 2 1 4719.2.a.c 1
273.g even 2 1 507.2.a.a 1
273.o odd 4 2 507.2.b.a 2
273.u even 6 2 507.2.e.b 2
273.bn even 6 2 507.2.e.a 2
273.ca odd 12 4 507.2.j.e 4
1092.d odd 2 1 8112.2.a.s 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
39.2.a.a 1 21.c even 2 1
117.2.a.a 1 7.b odd 2 1
507.2.a.a 1 273.g even 2 1
507.2.b.a 2 273.o odd 4 2
507.2.e.a 2 273.bn even 6 2
507.2.e.b 2 273.u even 6 2
507.2.j.e 4 273.ca odd 12 4
624.2.a.i 1 84.h odd 2 1
975.2.a.f 1 105.g even 2 1
975.2.c.f 2 105.k odd 4 2
1053.2.e.b 2 63.o even 6 2
1053.2.e.d 2 63.l odd 6 2
1521.2.a.e 1 91.b odd 2 1
1521.2.b.b 2 91.i even 4 2
1872.2.a.h 1 28.d even 2 1
1911.2.a.f 1 3.b odd 2 1
2496.2.a.e 1 168.e odd 2 1
2496.2.a.q 1 168.i even 2 1
2925.2.a.p 1 35.c odd 2 1
2925.2.c.e 2 35.f even 4 2
4719.2.a.c 1 231.h odd 2 1
5733.2.a.e 1 1.a even 1 1 trivial
7488.2.a.bl 1 56.h odd 2 1
7488.2.a.by 1 56.e even 2 1
8112.2.a.s 1 1092.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5733))$$:

 $$T_{2} + 1$$ T2 + 1 $$T_{5} - 2$$ T5 - 2 $$T_{11} + 4$$ T11 + 4 $$T_{17} - 2$$ T17 - 2 $$T_{19}$$ T19 $$T_{31} + 4$$ T31 + 4

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T + 1$$
$3$ $$T$$
$5$ $$T - 2$$
$7$ $$T$$
$11$ $$T + 4$$
$13$ $$T + 1$$
$17$ $$T - 2$$
$19$ $$T$$
$23$ $$T$$
$29$ $$T - 10$$
$31$ $$T + 4$$
$37$ $$T + 2$$
$41$ $$T - 6$$
$43$ $$T + 12$$
$47$ $$T$$
$53$ $$T + 6$$
$59$ $$T - 12$$
$61$ $$T - 2$$
$67$ $$T + 8$$
$71$ $$T$$
$73$ $$T + 2$$
$79$ $$T - 8$$
$83$ $$T - 4$$
$89$ $$T + 2$$
$97$ $$T + 10$$