Properties

 Label 950.2.a.e Level $950$ Weight $2$ Character orbit 950.a Self dual yes Analytic conductor $7.586$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(1,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2 q^{9}+O(q^{10})$$ q + q^2 + q^3 + q^4 + q^6 + q^7 + q^8 - 2 * q^9 $$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2 q^{9} + q^{12} + 3 q^{13} + q^{14} + q^{16} + 7 q^{17} - 2 q^{18} - q^{19} + q^{21} + 5 q^{23} + q^{24} + 3 q^{26} - 5 q^{27} + q^{28} - 5 q^{29} + 10 q^{31} + q^{32} + 7 q^{34} - 2 q^{36} - 2 q^{37} - q^{38} + 3 q^{39} + 2 q^{41} + q^{42} - 6 q^{43} + 5 q^{46} + q^{48} - 6 q^{49} + 7 q^{51} + 3 q^{52} - 9 q^{53} - 5 q^{54} + q^{56} - q^{57} - 5 q^{58} - 7 q^{59} - 4 q^{61} + 10 q^{62} - 2 q^{63} + q^{64} - 7 q^{67} + 7 q^{68} + 5 q^{69} - 2 q^{72} + 9 q^{73} - 2 q^{74} - q^{76} + 3 q^{78} - 10 q^{79} + q^{81} + 2 q^{82} + 2 q^{83} + q^{84} - 6 q^{86} - 5 q^{87} - 10 q^{89} + 3 q^{91} + 5 q^{92} + 10 q^{93} + q^{96} + 18 q^{97} - 6 q^{98}+O(q^{100})$$ q + q^2 + q^3 + q^4 + q^6 + q^7 + q^8 - 2 * q^9 + q^12 + 3 * q^13 + q^14 + q^16 + 7 * q^17 - 2 * q^18 - q^19 + q^21 + 5 * q^23 + q^24 + 3 * q^26 - 5 * q^27 + q^28 - 5 * q^29 + 10 * q^31 + q^32 + 7 * q^34 - 2 * q^36 - 2 * q^37 - q^38 + 3 * q^39 + 2 * q^41 + q^42 - 6 * q^43 + 5 * q^46 + q^48 - 6 * q^49 + 7 * q^51 + 3 * q^52 - 9 * q^53 - 5 * q^54 + q^56 - q^57 - 5 * q^58 - 7 * q^59 - 4 * q^61 + 10 * q^62 - 2 * q^63 + q^64 - 7 * q^67 + 7 * q^68 + 5 * q^69 - 2 * q^72 + 9 * q^73 - 2 * q^74 - q^76 + 3 * q^78 - 10 * q^79 + q^81 + 2 * q^82 + 2 * q^83 + q^84 - 6 * q^86 - 5 * q^87 - 10 * q^89 + 3 * q^91 + 5 * q^92 + 10 * q^93 + q^96 + 18 * q^97 - 6 * 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.

comment: embeddings in the coefficient field

gp: mfembed(f)

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 1.00000 1.00000 0 1.00000 1.00000 1.00000 −2.00000 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
$$2$$ $$-1$$
$$5$$ $$+1$$
$$19$$ $$+1$$

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 950.2.a.e 1
3.b odd 2 1 8550.2.a.l 1
4.b odd 2 1 7600.2.a.g 1
5.b even 2 1 190.2.a.a 1
5.c odd 4 2 950.2.b.d 2
15.d odd 2 1 1710.2.a.r 1
20.d odd 2 1 1520.2.a.g 1
35.c odd 2 1 9310.2.a.i 1
40.e odd 2 1 6080.2.a.i 1
40.f even 2 1 6080.2.a.r 1
95.d odd 2 1 3610.2.a.h 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.2.a.a 1 5.b even 2 1
950.2.a.e 1 1.a even 1 1 trivial
950.2.b.d 2 5.c odd 4 2
1520.2.a.g 1 20.d odd 2 1
1710.2.a.r 1 15.d odd 2 1
3610.2.a.h 1 95.d odd 2 1
6080.2.a.i 1 40.e odd 2 1
6080.2.a.r 1 40.f even 2 1
7600.2.a.g 1 4.b odd 2 1
8550.2.a.l 1 3.b odd 2 1
9310.2.a.i 1 35.c odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(950))$$:

 $$T_{3} - 1$$ T3 - 1 $$T_{7} - 1$$ T7 - 1 $$T_{11}$$ T11

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T - 1$$
$3$ $$T - 1$$
$5$ $$T$$
$7$ $$T - 1$$
$11$ $$T$$
$13$ $$T - 3$$
$17$ $$T - 7$$
$19$ $$T + 1$$
$23$ $$T - 5$$
$29$ $$T + 5$$
$31$ $$T - 10$$
$37$ $$T + 2$$
$41$ $$T - 2$$
$43$ $$T + 6$$
$47$ $$T$$
$53$ $$T + 9$$
$59$ $$T + 7$$
$61$ $$T + 4$$
$67$ $$T + 7$$
$71$ $$T$$
$73$ $$T - 9$$
$79$ $$T + 10$$
$83$ $$T - 2$$
$89$ $$T + 10$$
$97$ $$T - 18$$