# Properties

 Label 15488.2.a.u Level $15488$ Weight $2$ Character orbit 15488.a Self dual yes Analytic conductor $123.672$ Dimension $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15488,2,Mod(1,15488)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15488, 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("15488.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$15488 = 2^{7} \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 15488.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: $$123.672302651$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: not computed 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)

 $$f(q)$$ $$=$$ $$q + 2 q^{3} - 2 q^{5} - 4 q^{7} + q^{9}+O(q^{10})$$ q + 2 * q^3 - 2 * q^5 - 4 * q^7 + q^9 $$q + 2 q^{3} - 2 q^{5} - 4 q^{7} + q^{9} + 2 q^{13} - 4 q^{15} + 2 q^{17} - 2 q^{19} - 8 q^{21} - 4 q^{23} - q^{25} - 4 q^{27} - 6 q^{29} + 8 q^{35} - 10 q^{37} + 4 q^{39} + 6 q^{41} - 6 q^{43} - 2 q^{45} + 8 q^{47} + 9 q^{49} + 4 q^{51} + 6 q^{53} - 4 q^{57} + 14 q^{59} + 2 q^{61} - 4 q^{63} - 4 q^{65} + 10 q^{67} - 8 q^{69} - 12 q^{71} - 14 q^{73} - 2 q^{75} - 8 q^{79} - 11 q^{81} + 6 q^{83} - 4 q^{85} - 12 q^{87} - 2 q^{89} - 8 q^{91} + 4 q^{95} - 2 q^{97}+O(q^{100})$$ q + 2 * q^3 - 2 * q^5 - 4 * q^7 + q^9 + 2 * q^13 - 4 * q^15 + 2 * q^17 - 2 * q^19 - 8 * q^21 - 4 * q^23 - q^25 - 4 * q^27 - 6 * q^29 + 8 * q^35 - 10 * q^37 + 4 * q^39 + 6 * q^41 - 6 * q^43 - 2 * q^45 + 8 * q^47 + 9 * q^49 + 4 * q^51 + 6 * q^53 - 4 * q^57 + 14 * q^59 + 2 * q^61 - 4 * q^63 - 4 * q^65 + 10 * q^67 - 8 * q^69 - 12 * q^71 - 14 * q^73 - 2 * q^75 - 8 * q^79 - 11 * q^81 + 6 * q^83 - 4 * q^85 - 12 * q^87 - 2 * q^89 - 8 * q^91 + 4 * q^95 - 2 * q^97

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$+1$$
$$11$$ $$-1$$

## Inner twists

Inner twists of this newform have not been computed.

## Twists

Twists of this newform have not been computed.