Properties

 Label 4950.2.a.bc Level $4950$ Weight $2$ Character orbit 4950.a Self dual yes Analytic conductor $39.526$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4950.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$39.5259490005$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 110) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{4} - 3 q^{7} + q^{8}+O(q^{10})$$ q + q^2 + q^4 - 3 * q^7 + q^8 $$q + q^{2} + q^{4} - 3 q^{7} + q^{8} - q^{11} + 6 q^{13} - 3 q^{14} + q^{16} - 7 q^{17} + 5 q^{19} - q^{22} - 6 q^{23} + 6 q^{26} - 3 q^{28} - 5 q^{29} - 3 q^{31} + q^{32} - 7 q^{34} - 3 q^{37} + 5 q^{38} - 2 q^{41} - 4 q^{43} - q^{44} - 6 q^{46} - 2 q^{47} + 2 q^{49} + 6 q^{52} - q^{53} - 3 q^{56} - 5 q^{58} + 10 q^{59} + 7 q^{61} - 3 q^{62} + q^{64} - 8 q^{67} - 7 q^{68} - 7 q^{71} - 14 q^{73} - 3 q^{74} + 5 q^{76} + 3 q^{77} + 10 q^{79} - 2 q^{82} - 6 q^{83} - 4 q^{86} - q^{88} + 15 q^{89} - 18 q^{91} - 6 q^{92} - 2 q^{94} + 12 q^{97} + 2 q^{98}+O(q^{100})$$ q + q^2 + q^4 - 3 * q^7 + q^8 - q^11 + 6 * q^13 - 3 * q^14 + q^16 - 7 * q^17 + 5 * q^19 - q^22 - 6 * q^23 + 6 * q^26 - 3 * q^28 - 5 * q^29 - 3 * q^31 + q^32 - 7 * q^34 - 3 * q^37 + 5 * q^38 - 2 * q^41 - 4 * q^43 - q^44 - 6 * q^46 - 2 * q^47 + 2 * q^49 + 6 * q^52 - q^53 - 3 * q^56 - 5 * q^58 + 10 * q^59 + 7 * q^61 - 3 * q^62 + q^64 - 8 * q^67 - 7 * q^68 - 7 * q^71 - 14 * q^73 - 3 * q^74 + 5 * q^76 + 3 * q^77 + 10 * q^79 - 2 * q^82 - 6 * q^83 - 4 * q^86 - q^88 + 15 * q^89 - 18 * q^91 - 6 * q^92 - 2 * q^94 + 12 * q^97 + 2 * 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 −3.00000 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
$$2$$ $$-1$$
$$3$$ $$-1$$
$$5$$ $$1$$
$$11$$ $$1$$

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 4950.2.a.bc 1
3.b odd 2 1 550.2.a.f 1
5.b even 2 1 990.2.a.d 1
5.c odd 4 2 4950.2.c.m 2
12.b even 2 1 4400.2.a.l 1
15.d odd 2 1 110.2.a.b 1
15.e even 4 2 550.2.b.a 2
20.d odd 2 1 7920.2.a.d 1
33.d even 2 1 6050.2.a.bj 1
60.h even 2 1 880.2.a.i 1
60.l odd 4 2 4400.2.b.i 2
105.g even 2 1 5390.2.a.bf 1
120.i odd 2 1 3520.2.a.y 1
120.m even 2 1 3520.2.a.h 1
165.d even 2 1 1210.2.a.b 1
660.g odd 2 1 9680.2.a.x 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
110.2.a.b 1 15.d odd 2 1
550.2.a.f 1 3.b odd 2 1
550.2.b.a 2 15.e even 4 2
880.2.a.i 1 60.h even 2 1
990.2.a.d 1 5.b even 2 1
1210.2.a.b 1 165.d even 2 1
3520.2.a.h 1 120.m even 2 1
3520.2.a.y 1 120.i odd 2 1
4400.2.a.l 1 12.b even 2 1
4400.2.b.i 2 60.l odd 4 2
4950.2.a.bc 1 1.a even 1 1 trivial
4950.2.c.m 2 5.c odd 4 2
5390.2.a.bf 1 105.g even 2 1
6050.2.a.bj 1 33.d even 2 1
7920.2.a.d 1 20.d odd 2 1
9680.2.a.x 1 660.g odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(4950))$$:

 $$T_{7} + 3$$ T7 + 3 $$T_{13} - 6$$ T13 - 6 $$T_{17} + 7$$ T17 + 7 $$T_{19} - 5$$ T19 - 5 $$T_{23} + 6$$ T23 + 6

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T - 1$$
$3$ $$T$$
$5$ $$T$$
$7$ $$T + 3$$
$11$ $$T + 1$$
$13$ $$T - 6$$
$17$ $$T + 7$$
$19$ $$T - 5$$
$23$ $$T + 6$$
$29$ $$T + 5$$
$31$ $$T + 3$$
$37$ $$T + 3$$
$41$ $$T + 2$$
$43$ $$T + 4$$
$47$ $$T + 2$$
$53$ $$T + 1$$
$59$ $$T - 10$$
$61$ $$T - 7$$
$67$ $$T + 8$$
$71$ $$T + 7$$
$73$ $$T + 14$$
$79$ $$T - 10$$
$83$ $$T + 6$$
$89$ $$T - 15$$
$97$ $$T - 12$$