# Properties

 Label 46410.2.a.ck Level $46410$ Weight $2$ Character orbit 46410.a Self dual yes Analytic conductor $370.586$ 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] = [46410,2,Mod(1,46410)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46410, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("46410.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$46410 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 46410.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: $$370.585715781$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes 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)

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} + q^{9}+O(q^{10})$$ q + q^2 + q^3 + q^4 + q^5 + q^6 - q^7 + q^8 + q^9 $$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + q^{10} - 4 q^{11} + q^{12} + q^{13} - q^{14} + q^{15} + q^{16} + q^{17} + q^{18} + 4 q^{19} + q^{20} - q^{21} - 4 q^{22} + 8 q^{23} + q^{24} + q^{25} + q^{26} + q^{27} - q^{28} - 2 q^{29} + q^{30} + q^{32} - 4 q^{33} + q^{34} - q^{35} + q^{36} + 6 q^{37} + 4 q^{38} + q^{39} + q^{40} + 10 q^{41} - q^{42} - 4 q^{43} - 4 q^{44} + q^{45} + 8 q^{46} + q^{48} + q^{49} + q^{50} + q^{51} + q^{52} - 10 q^{53} + q^{54} - 4 q^{55} - q^{56} + 4 q^{57} - 2 q^{58} - 4 q^{59} + q^{60} - 2 q^{61} - q^{63} + q^{64} + q^{65} - 4 q^{66} + 4 q^{67} + q^{68} + 8 q^{69} - q^{70} + 8 q^{71} + q^{72} + 10 q^{73} + 6 q^{74} + q^{75} + 4 q^{76} + 4 q^{77} + q^{78} - 16 q^{79} + q^{80} + q^{81} + 10 q^{82} - 12 q^{83} - q^{84} + q^{85} - 4 q^{86} - 2 q^{87} - 4 q^{88} + 10 q^{89} + q^{90} - q^{91} + 8 q^{92} + 4 q^{95} + q^{96} + 2 q^{97} + q^{98} - 4 q^{99}+O(q^{100})$$ q + q^2 + q^3 + q^4 + q^5 + q^6 - q^7 + q^8 + q^9 + q^10 - 4 * q^11 + q^12 + q^13 - q^14 + q^15 + q^16 + q^17 + q^18 + 4 * q^19 + q^20 - q^21 - 4 * q^22 + 8 * q^23 + q^24 + q^25 + q^26 + q^27 - q^28 - 2 * q^29 + q^30 + q^32 - 4 * q^33 + q^34 - q^35 + q^36 + 6 * q^37 + 4 * q^38 + q^39 + q^40 + 10 * q^41 - q^42 - 4 * q^43 - 4 * q^44 + q^45 + 8 * q^46 + q^48 + q^49 + q^50 + q^51 + q^52 - 10 * q^53 + q^54 - 4 * q^55 - q^56 + 4 * q^57 - 2 * q^58 - 4 * q^59 + q^60 - 2 * q^61 - q^63 + q^64 + q^65 - 4 * q^66 + 4 * q^67 + q^68 + 8 * q^69 - q^70 + 8 * q^71 + q^72 + 10 * q^73 + 6 * q^74 + q^75 + 4 * q^76 + 4 * q^77 + q^78 - 16 * q^79 + q^80 + q^81 + 10 * q^82 - 12 * q^83 - q^84 + q^85 - 4 * q^86 - 2 * q^87 - 4 * q^88 + 10 * q^89 + q^90 - q^91 + 8 * q^92 + 4 * q^95 + q^96 + 2 * q^97 + q^98 - 4 * q^99

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$-1$$
$$3$$ $$-1$$
$$5$$ $$-1$$
$$7$$ $$+1$$
$$13$$ $$-1$$
$$17$$ $$-1$$

## Inner twists

This newform does not admit any (nontrivial) inner twists.

## Twists

Twists of this newform have not been computed.