Properties

 Label 5850.2.a.e Level $5850$ Weight $2$ Character orbit 5850.a Self dual yes Analytic conductor $46.712$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5850.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$46.7124851824$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} + q^{4} - 4 q^{7} - q^{8}+O(q^{10})$$ q - q^2 + q^4 - 4 * q^7 - q^8 $$q - q^{2} + q^{4} - 4 q^{7} - q^{8} + 6 q^{11} + q^{13} + 4 q^{14} + q^{16} + 4 q^{17} + 2 q^{19} - 6 q^{22} + 6 q^{23} - q^{26} - 4 q^{28} + 10 q^{29} + 4 q^{31} - q^{32} - 4 q^{34} - 6 q^{37} - 2 q^{38} - 10 q^{41} + 6 q^{44} - 6 q^{46} - 8 q^{47} + 9 q^{49} + q^{52} + 6 q^{53} + 4 q^{56} - 10 q^{58} + 6 q^{59} - 6 q^{61} - 4 q^{62} + q^{64} - 12 q^{67} + 4 q^{68} + 2 q^{73} + 6 q^{74} + 2 q^{76} - 24 q^{77} - 8 q^{79} + 10 q^{82} + 4 q^{83} - 6 q^{88} - 14 q^{89} - 4 q^{91} + 6 q^{92} + 8 q^{94} + 14 q^{97} - 9 q^{98}+O(q^{100})$$ q - q^2 + q^4 - 4 * q^7 - q^8 + 6 * q^11 + q^13 + 4 * q^14 + q^16 + 4 * q^17 + 2 * q^19 - 6 * q^22 + 6 * q^23 - q^26 - 4 * q^28 + 10 * q^29 + 4 * q^31 - q^32 - 4 * q^34 - 6 * q^37 - 2 * q^38 - 10 * q^41 + 6 * q^44 - 6 * q^46 - 8 * q^47 + 9 * q^49 + q^52 + 6 * q^53 + 4 * q^56 - 10 * q^58 + 6 * q^59 - 6 * q^61 - 4 * q^62 + q^64 - 12 * q^67 + 4 * q^68 + 2 * q^73 + 6 * q^74 + 2 * q^76 - 24 * q^77 - 8 * q^79 + 10 * q^82 + 4 * q^83 - 6 * q^88 - 14 * q^89 - 4 * q^91 + 6 * q^92 + 8 * q^94 + 14 * q^97 - 9 * q^98

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 0 0 −4.00000 −1.00000 0 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$1$$
$$3$$ $$-1$$
$$5$$ $$-1$$
$$13$$ $$-1$$

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 5850.2.a.e 1
3.b odd 2 1 1950.2.a.v 1
5.b even 2 1 5850.2.a.cc 1
5.c odd 4 2 1170.2.e.c 2
15.d odd 2 1 1950.2.a.d 1
15.e even 4 2 390.2.e.d 2
60.l odd 4 2 3120.2.l.i 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
390.2.e.d 2 15.e even 4 2
1170.2.e.c 2 5.c odd 4 2
1950.2.a.d 1 15.d odd 2 1
1950.2.a.v 1 3.b odd 2 1
3120.2.l.i 2 60.l odd 4 2
5850.2.a.e 1 1.a even 1 1 trivial
5850.2.a.cc 1 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5850))$$:

 $$T_{7} + 4$$ T7 + 4 $$T_{11} - 6$$ T11 - 6 $$T_{17} - 4$$ T17 - 4 $$T_{23} - 6$$ T23 - 6 $$T_{31} - 4$$ T31 - 4

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T + 1$$
$3$ $$T$$
$5$ $$T$$
$7$ $$T + 4$$
$11$ $$T - 6$$
$13$ $$T - 1$$
$17$ $$T - 4$$
$19$ $$T - 2$$
$23$ $$T - 6$$
$29$ $$T - 10$$
$31$ $$T - 4$$
$37$ $$T + 6$$
$41$ $$T + 10$$
$43$ $$T$$
$47$ $$T + 8$$
$53$ $$T - 6$$
$59$ $$T - 6$$
$61$ $$T + 6$$
$67$ $$T + 12$$
$71$ $$T$$
$73$ $$T - 2$$
$79$ $$T + 8$$
$83$ $$T - 4$$
$89$ $$T + 14$$
$97$ $$T - 14$$