# Properties

 Label 16245.2.a.c Level $16245$ Weight $2$ Character orbit 16245.a Self dual yes Analytic conductor $129.717$ Dimension $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16245,2,Mod(1,16245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16245, 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("16245.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$16245 = 3^{2} \cdot 5 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 16245.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: $$129.716978084$$ 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)

 $$f(q)$$ $$=$$ $$q - q^{2} - q^{4} - q^{5} + 3 q^{8}+O(q^{10})$$ q - q^2 - q^4 - q^5 + 3 * q^8 $$q - q^{2} - q^{4} - q^{5} + 3 q^{8} + q^{10} + 4 q^{11} + 2 q^{13} - q^{16} - 2 q^{17} + q^{20} - 4 q^{22} + q^{25} - 2 q^{26} - 2 q^{29} - 5 q^{32} + 2 q^{34} + 10 q^{37} - 3 q^{40} + 10 q^{41} + 4 q^{43} - 4 q^{44} - 8 q^{47} - 7 q^{49} - q^{50} - 2 q^{52} - 10 q^{53} - 4 q^{55} + 2 q^{58} - 4 q^{59} - 2 q^{61} + 7 q^{64} - 2 q^{65} - 12 q^{67} + 2 q^{68} - 8 q^{71} + 10 q^{73} - 10 q^{74} + q^{80} - 10 q^{82} - 12 q^{83} + 2 q^{85} - 4 q^{86} + 12 q^{88} - 6 q^{89} + 8 q^{94} - 2 q^{97} + 7 q^{98}+O(q^{100})$$ q - q^2 - q^4 - q^5 + 3 * q^8 + q^10 + 4 * q^11 + 2 * q^13 - q^16 - 2 * q^17 + q^20 - 4 * q^22 + q^25 - 2 * q^26 - 2 * q^29 - 5 * q^32 + 2 * q^34 + 10 * q^37 - 3 * q^40 + 10 * q^41 + 4 * q^43 - 4 * q^44 - 8 * q^47 - 7 * q^49 - q^50 - 2 * q^52 - 10 * q^53 - 4 * q^55 + 2 * q^58 - 4 * q^59 - 2 * q^61 + 7 * q^64 - 2 * q^65 - 12 * q^67 + 2 * q^68 - 8 * q^71 + 10 * q^73 - 10 * q^74 + q^80 - 10 * q^82 - 12 * q^83 + 2 * q^85 - 4 * q^86 + 12 * q^88 - 6 * q^89 + 8 * q^94 - 2 * q^97 + 7 * q^98

## Atkin-Lehner signs

$$p$$ Sign
$$3$$ $$-1$$
$$5$$ $$+1$$
$$19$$ $$-1$$

## Inner twists

Inner twists of this newform have not been computed.

## Twists

Twists of this newform have not been computed.