Properties

 Label 7105.2.a.b Level $7105$ Weight $2$ Character orbit 7105.a Self dual yes Analytic conductor $56.734$ Analytic rank $1$ 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] = [7105,2,Mod(1,7105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7105.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$7105 = 5 \cdot 7^{2} \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7105.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: $$56.7337106361$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 145) 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)

 $$f(q)$$ $$=$$ $$q - q^{2} - q^{4} + q^{5} + 3 q^{8} - 3 q^{9}+O(q^{10})$$ q - q^2 - q^4 + q^5 + 3 * q^8 - 3 * q^9 $$q - q^{2} - q^{4} + q^{5} + 3 q^{8} - 3 q^{9} - q^{10} - 6 q^{11} - 2 q^{13} - q^{16} + 2 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} + 6 q^{22} + 2 q^{23} + q^{25} + 2 q^{26} - q^{29} - 2 q^{31} - 5 q^{32} - 2 q^{34} + 3 q^{36} + 10 q^{37} - 2 q^{38} + 3 q^{40} - 2 q^{41} + 8 q^{43} + 6 q^{44} - 3 q^{45} - 2 q^{46} + 12 q^{47} - q^{50} + 2 q^{52} - 6 q^{53} - 6 q^{55} + q^{58} + 8 q^{59} + 6 q^{61} + 2 q^{62} + 7 q^{64} - 2 q^{65} + 2 q^{67} - 2 q^{68} - 12 q^{71} - 9 q^{72} + 6 q^{73} - 10 q^{74} - 2 q^{76} - 10 q^{79} - q^{80} + 9 q^{81} + 2 q^{82} + 14 q^{83} + 2 q^{85} - 8 q^{86} - 18 q^{88} - 18 q^{89} + 3 q^{90} - 2 q^{92} - 12 q^{94} + 2 q^{95} - 2 q^{97} + 18 q^{99}+O(q^{100})$$ q - q^2 - q^4 + q^5 + 3 * q^8 - 3 * q^9 - q^10 - 6 * q^11 - 2 * q^13 - q^16 + 2 * q^17 + 3 * q^18 + 2 * q^19 - q^20 + 6 * q^22 + 2 * q^23 + q^25 + 2 * q^26 - q^29 - 2 * q^31 - 5 * q^32 - 2 * q^34 + 3 * q^36 + 10 * q^37 - 2 * q^38 + 3 * q^40 - 2 * q^41 + 8 * q^43 + 6 * q^44 - 3 * q^45 - 2 * q^46 + 12 * q^47 - q^50 + 2 * q^52 - 6 * q^53 - 6 * q^55 + q^58 + 8 * q^59 + 6 * q^61 + 2 * q^62 + 7 * q^64 - 2 * q^65 + 2 * q^67 - 2 * q^68 - 12 * q^71 - 9 * q^72 + 6 * q^73 - 10 * q^74 - 2 * q^76 - 10 * q^79 - q^80 + 9 * q^81 + 2 * q^82 + 14 * q^83 + 2 * q^85 - 8 * q^86 - 18 * q^88 - 18 * q^89 + 3 * q^90 - 2 * q^92 - 12 * q^94 + 2 * q^95 - 2 * q^97 + 18 * q^99

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 0 −1.00000 1.00000 0 0 3.00000 −3.00000 −1.00000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

$$p$$ Sign
$$5$$ $$-1$$
$$7$$ $$-1$$
$$29$$ $$1$$

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 7105.2.a.b 1
7.b odd 2 1 145.2.a.a 1
21.c even 2 1 1305.2.a.f 1
28.d even 2 1 2320.2.a.e 1
35.c odd 2 1 725.2.a.a 1
35.f even 4 2 725.2.b.a 2
56.e even 2 1 9280.2.a.o 1
56.h odd 2 1 9280.2.a.l 1
105.g even 2 1 6525.2.a.d 1
203.c odd 2 1 4205.2.a.a 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
145.2.a.a 1 7.b odd 2 1
725.2.a.a 1 35.c odd 2 1
725.2.b.a 2 35.f even 4 2
1305.2.a.f 1 21.c even 2 1
2320.2.a.e 1 28.d even 2 1
4205.2.a.a 1 203.c odd 2 1
6525.2.a.d 1 105.g even 2 1
7105.2.a.b 1 1.a even 1 1 trivial
9280.2.a.l 1 56.h odd 2 1
9280.2.a.o 1 56.e even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(7105))$$:

 $$T_{2} + 1$$ T2 + 1 $$T_{3}$$ T3 $$T_{17} - 2$$ T17 - 2

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T + 1$$
$3$ $$T$$
$5$ $$T - 1$$
$7$ $$T$$
$11$ $$T + 6$$
$13$ $$T + 2$$
$17$ $$T - 2$$
$19$ $$T - 2$$
$23$ $$T - 2$$
$29$ $$T + 1$$
$31$ $$T + 2$$
$37$ $$T - 10$$
$41$ $$T + 2$$
$43$ $$T - 8$$
$47$ $$T - 12$$
$53$ $$T + 6$$
$59$ $$T - 8$$
$61$ $$T - 6$$
$67$ $$T - 2$$
$71$ $$T + 12$$
$73$ $$T - 6$$
$79$ $$T + 10$$
$83$ $$T - 14$$
$89$ $$T + 18$$
$97$ $$T + 2$$