Properties

Label 1890.2.bk.b
Level 1890
Weight 2
Character orbit 1890.bk
Analytic conductor 15.092
Analytic rank 0
Dimension 28
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(15.0917259820\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 28q - 28q^{4} + 14q^{5} + 8q^{7} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 28q - 28q^{4} + 14q^{5} + 8q^{7} + 28q^{16} - 6q^{17} - 6q^{19} - 14q^{20} - 6q^{22} - 30q^{23} - 14q^{25} + 12q^{26} - 8q^{28} + 4q^{35} + 4q^{37} + 6q^{38} + 18q^{41} + 28q^{43} - 18q^{46} - 60q^{47} - 20q^{49} - 42q^{53} + 6q^{58} + 48q^{59} - 12q^{62} - 28q^{64} + 80q^{67} + 6q^{68} + 6q^{70} + 6q^{73} + 6q^{76} + 18q^{77} - 4q^{79} + 14q^{80} + 24q^{82} - 18q^{83} + 6q^{85} + 96q^{86} + 6q^{88} + 6q^{89} + 66q^{91} + 30q^{92} + 72q^{97} - 24q^{98} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
341.1 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 2.48469 0.909025i 1.00000i 0 0.866025 0.500000i
341.2 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 1.55779 + 2.13853i 1.00000i 0 0.866025 0.500000i
341.3 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −2.21694 1.44401i 1.00000i 0 −0.866025 + 0.500000i
341.4 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 0.145275 2.64176i 1.00000i 0 −0.866025 + 0.500000i
341.5 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 2.55256 + 0.696025i 1.00000i 0 −0.866025 + 0.500000i
341.6 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −0.323069 2.62595i 1.00000i 0 0.866025 0.500000i
341.7 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −1.17317 + 2.37143i 1.00000i 0 −0.866025 + 0.500000i
341.8 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −1.91453 + 1.82609i 1.00000i 0 0.866025 0.500000i
341.9 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 0.281867 + 2.63069i 1.00000i 0 −0.866025 + 0.500000i
341.10 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 2.64078 + 0.162142i 1.00000i 0 −0.866025 + 0.500000i
341.11 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 2.57280 0.617016i 1.00000i 0 0.866025 0.500000i
341.12 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 0.408654 + 2.61400i 1.00000i 0 0.866025 0.500000i
341.13 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −1.96242 1.77452i 1.00000i 0 −0.866025 + 0.500000i
341.14 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −1.05428 2.42662i 1.00000i 0 0.866025 0.500000i
521.1 1.00000i 0 −1.00000 0.500000 0.866025i 0 2.48469 + 0.909025i 1.00000i 0 0.866025 + 0.500000i
521.2 1.00000i 0 −1.00000 0.500000 0.866025i 0 1.55779 2.13853i 1.00000i 0 0.866025 + 0.500000i
521.3 1.00000i 0 −1.00000 0.500000 0.866025i 0 −2.21694 + 1.44401i 1.00000i 0 −0.866025 0.500000i
521.4 1.00000i 0 −1.00000 0.500000 0.866025i 0 0.145275 + 2.64176i 1.00000i 0 −0.866025 0.500000i
521.5 1.00000i 0 −1.00000 0.500000 0.866025i 0 2.55256 0.696025i 1.00000i 0 −0.866025 0.500000i
521.6 1.00000i 0 −1.00000 0.500000 0.866025i 0 −0.323069 + 2.62595i 1.00000i 0 0.866025 + 0.500000i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 521.14
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
63.i 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.bk.b 28
3.b odd 2 1 630.2.bk.b yes 28
7.d odd 6 1 1890.2.t.b 28
9.c even 3 1 630.2.t.b 28
9.d odd 6 1 1890.2.t.b 28
21.g even 6 1 630.2.t.b 28
63.i even 6 1 inner 1890.2.bk.b 28
63.t odd 6 1 630.2.bk.b yes 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.t.b 28 9.c even 3 1
630.2.t.b 28 21.g even 6 1
630.2.bk.b yes 28 3.b odd 2 1
630.2.bk.b yes 28 63.t odd 6 1
1890.2.t.b 28 7.d odd 6 1
1890.2.t.b 28 9.d odd 6 1
1890.2.bk.b 28 1.a even 1 1 trivial
1890.2.bk.b 28 63.i even 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{11}^{28} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(1890, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database