# Properties

 Label 1890.2.t.c Level 1890 Weight 2 Character orbit 1890.t Analytic conductor 15.092 Analytic rank 0 Dimension 32 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1890.t (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.0917259820$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(\zeta_{6})$$ Twist minimal: no (minimal twist has level 630) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## $q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$32q + 16q^{4} - 32q^{5} - 2q^{7} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$32q + 16q^{4} - 32q^{5} - 2q^{7} - 16q^{16} - 6q^{17} - 16q^{20} + 32q^{25} - 12q^{26} + 2q^{28} - 6q^{29} + 18q^{31} + 2q^{35} + 2q^{37} + 6q^{41} - 28q^{43} + 6q^{44} - 24q^{47} + 32q^{49} + 36q^{53} + 6q^{56} + 30q^{59} + 54q^{61} - 32q^{64} + 4q^{67} - 12q^{68} - 30q^{73} + 6q^{77} + 4q^{79} + 16q^{80} - 24q^{82} - 6q^{83} + 6q^{85} + 12q^{89} - 66q^{91} + 18q^{92} - 42q^{94} + 96q^{97} + 24q^{98} + O(q^{100})$$

## 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.

Label $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1151.1 −0.866025 0.500000i 0 0.500000 + 0.866025i −1.00000 0 0.104916 + 2.64367i 1.00000i 0 0.866025 + 0.500000i
1151.2 −0.866025 0.500000i 0 0.500000 + 0.866025i −1.00000 0 2.63859 + 0.194573i 1.00000i 0 0.866025 + 0.500000i
1151.3 −0.866025 0.500000i 0 0.500000 + 0.866025i −1.00000 0 1.13965 2.38772i 1.00000i 0 0.866025 + 0.500000i
1151.4 −0.866025 0.500000i 0 0.500000 + 0.866025i −1.00000 0 −1.89754 + 1.84373i 1.00000i 0 0.866025 + 0.500000i
1151.5 −0.866025 0.500000i 0 0.500000 + 0.866025i −1.00000 0 −2.46207 + 0.968625i 1.00000i 0 0.866025 + 0.500000i
1151.6 −0.866025 0.500000i 0 0.500000 + 0.866025i −1.00000 0 0.778946 2.52849i 1.00000i 0 0.866025 + 0.500000i
1151.7 −0.866025 0.500000i 0 0.500000 + 0.866025i −1.00000 0 2.26702 + 1.36404i 1.00000i 0 0.866025 + 0.500000i
1151.8 −0.866025 0.500000i 0 0.500000 + 0.866025i −1.00000 0 −2.20349 1.46446i 1.00000i 0 0.866025 + 0.500000i
1151.9 0.866025 + 0.500000i 0 0.500000 + 0.866025i −1.00000 0 −2.63727 0.211686i 1.00000i 0 −0.866025 0.500000i
1151.10 0.866025 + 0.500000i 0 0.500000 + 0.866025i −1.00000 0 2.60525 0.461188i 1.00000i 0 −0.866025 0.500000i
1151.11 0.866025 + 0.500000i 0 0.500000 + 0.866025i −1.00000 0 1.49710 + 2.18144i 1.00000i 0 −0.866025 0.500000i
1151.12 0.866025 + 0.500000i 0 0.500000 + 0.866025i −1.00000 0 −1.74301 1.99046i 1.00000i 0 −0.866025 0.500000i
1151.13 0.866025 + 0.500000i 0 0.500000 + 0.866025i −1.00000 0 −2.64561 + 0.0270445i 1.00000i 0 −0.866025 0.500000i
1151.14 0.866025 + 0.500000i 0 0.500000 + 0.866025i −1.00000 0 −1.80382 + 1.93552i 1.00000i 0 −0.866025 0.500000i
1151.15 0.866025 + 0.500000i 0 0.500000 + 0.866025i −1.00000 0 1.16109 2.37737i 1.00000i 0 −0.866025 0.500000i
1151.16 0.866025 + 0.500000i 0 0.500000 + 0.866025i −1.00000 0 2.20024 1.46933i 1.00000i 0 −0.866025 0.500000i
1601.1 −0.866025 + 0.500000i 0 0.500000 0.866025i −1.00000 0 0.104916 2.64367i 1.00000i 0 0.866025 0.500000i
1601.2 −0.866025 + 0.500000i 0 0.500000 0.866025i −1.00000 0 2.63859 0.194573i 1.00000i 0 0.866025 0.500000i
1601.3 −0.866025 + 0.500000i 0 0.500000 0.866025i −1.00000 0 1.13965 + 2.38772i 1.00000i 0 0.866025 0.500000i
1601.4 −0.866025 + 0.500000i 0 0.500000 0.866025i −1.00000 0 −1.89754 1.84373i 1.00000i 0 0.866025 0.500000i
See all 32 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1601.16 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
63.s even 6 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1890.2.t.c 32
3.b odd 2 1 630.2.t.c 32
7.d odd 6 1 1890.2.bk.c 32
9.c even 3 1 630.2.bk.c yes 32
9.d odd 6 1 1890.2.bk.c 32
21.g even 6 1 630.2.bk.c yes 32
63.k odd 6 1 630.2.t.c 32
63.s even 6 1 inner 1890.2.t.c 32

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.t.c 32 3.b odd 2 1
630.2.t.c 32 63.k odd 6 1
630.2.bk.c yes 32 9.c even 3 1
630.2.bk.c yes 32 21.g even 6 1
1890.2.t.c 32 1.a even 1 1 trivial
1890.2.t.c 32 63.s even 6 1 inner
1890.2.bk.c 32 7.d odd 6 1
1890.2.bk.c 32 9.d odd 6 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{11}^{32} + \cdots$$ acting on $$S_{2}^{\mathrm{new}}(1890, [\chi])$$.

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database