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

Downloads

Learn more about

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:

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