Properties

Label 1890.2.t.b
Level 1890
Weight 2
Character orbit 1890.t
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.t (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.

\(\operatorname{Tr}(f)(q) = \) \( 28q + 14q^{4} + 28q^{5} - 4q^{7} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 28q + 14q^{4} + 28q^{5} - 4q^{7} - 6q^{14} - 14q^{16} + 6q^{17} - 6q^{19} + 14q^{20} - 6q^{22} + 28q^{25} - 12q^{26} - 8q^{28} - 12q^{31} - 4q^{35} + 4q^{37} + 12q^{38} - 18q^{41} + 28q^{43} - 18q^{46} - 30q^{47} - 14q^{49} + 42q^{53} - 6q^{56} - 12q^{58} + 24q^{59} + 24q^{61} + 12q^{62} - 28q^{64} - 40q^{67} + 12q^{68} - 6q^{70} + 6q^{73} - 6q^{76} + 24q^{77} + 2q^{79} - 14q^{80} + 24q^{82} + 18q^{83} + 6q^{85} - 12q^{88} - 6q^{89} + 66q^{91} + 30q^{92} + 42q^{94} - 6q^{95} - 72q^{97} + 24q^{98} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1151.1 −0.866025 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −0.555567 2.58676i 1.00000i 0 −0.866025 0.500000i
1151.2 −0.866025 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −2.36047 1.19507i 1.00000i 0 −0.866025 0.500000i
1151.3 −0.866025 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −0.673503 + 2.55859i 1.00000i 0 −0.866025 0.500000i
1151.4 −0.866025 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −1.17997 + 2.36805i 1.00000i 0 −0.866025 0.500000i
1151.5 −0.866025 0.500000i 0 0.500000 + 0.866025i 1.00000 0 2.13731 + 1.55945i 1.00000i 0 −0.866025 0.500000i
1151.6 −0.866025 0.500000i 0 0.500000 + 0.866025i 1.00000 0 2.64030 + 0.169721i 1.00000i 0 −0.866025 0.500000i
1151.7 −0.866025 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −0.142082 2.64193i 1.00000i 0 −0.866025 0.500000i
1151.8 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −1.57438 2.12634i 1.00000i 0 0.866025 + 0.500000i
1151.9 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 2.05946 + 1.66090i 1.00000i 0 0.866025 + 0.500000i
1151.10 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 2.53870 0.744985i 1.00000i 0 0.866025 + 0.500000i
1151.11 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −2.11261 1.59276i 1.00000i 0 0.866025 + 0.500000i
1151.12 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −1.82075 + 1.91960i 1.00000i 0 0.866025 + 0.500000i
1151.13 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 1.07313 + 2.41835i 1.00000i 0 0.866025 + 0.500000i
1151.14 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −2.02958 + 1.69729i 1.00000i 0 0.866025 + 0.500000i
1601.1 −0.866025 + 0.500000i 0 0.500000 0.866025i 1.00000 0 −0.555567 + 2.58676i 1.00000i 0 −0.866025 + 0.500000i
1601.2 −0.866025 + 0.500000i 0 0.500000 0.866025i 1.00000 0 −2.36047 + 1.19507i 1.00000i 0 −0.866025 + 0.500000i
1601.3 −0.866025 + 0.500000i 0 0.500000 0.866025i 1.00000 0 −0.673503 2.55859i 1.00000i 0 −0.866025 + 0.500000i
1601.4 −0.866025 + 0.500000i 0 0.500000 0.866025i 1.00000 0 −1.17997 2.36805i 1.00000i 0 −0.866025 + 0.500000i
1601.5 −0.866025 + 0.500000i 0 0.500000 0.866025i 1.00000 0 2.13731 1.55945i 1.00000i 0 −0.866025 + 0.500000i
1601.6 −0.866025 + 0.500000i 0 0.500000 0.866025i 1.00000 0 2.64030 0.169721i 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 1601.14
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.b 28
3.b odd 2 1 630.2.t.b 28
7.d odd 6 1 1890.2.bk.b 28
9.c even 3 1 630.2.bk.b yes 28
9.d odd 6 1 1890.2.bk.b 28
21.g even 6 1 630.2.bk.b yes 28
63.k odd 6 1 630.2.t.b 28
63.s even 6 1 inner 1890.2.t.b 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.t.b 28 3.b odd 2 1
630.2.t.b 28 63.k odd 6 1
630.2.bk.b yes 28 9.c even 3 1
630.2.bk.b yes 28 21.g even 6 1
1890.2.t.b 28 1.a even 1 1 trivial
1890.2.t.b 28 63.s even 6 1 inner
1890.2.bk.b 28 7.d odd 6 1
1890.2.bk.b 28 9.d odd 6 1

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