Properties

Label 1143.3.b.a
Level $1143$
Weight $3$
Character orbit 1143.b
Analytic conductor $31.144$
Analytic rank $0$
Dimension $84$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1143.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.1444942164\)
Analytic rank: \(0\)
Dimension: \(84\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 84q - 160q^{4} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 84q - 160q^{4} - 48q^{10} + 16q^{13} + 360q^{16} + 64q^{19} - 8q^{22} - 388q^{25} - 120q^{28} - 160q^{31} + 192q^{34} - 152q^{37} + 208q^{40} - 24q^{43} + 56q^{46} + 564q^{49} - 80q^{52} + 136q^{55} - 136q^{58} + 168q^{61} - 736q^{64} + 168q^{67} - 608q^{70} + 80q^{73} - 32q^{76} - 168q^{79} + 528q^{82} + 288q^{85} - 392q^{88} + 176q^{91} + 176q^{94} - 120q^{97} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
890.1 3.88526i 0 −11.0952 2.03195i 0 −5.71279 27.5669i 0 7.89464
890.2 3.86719i 0 −10.9551 9.44547i 0 11.3204 26.8969i 0 −36.5274
890.3 3.83653i 0 −10.7190 7.45843i 0 0.844054 25.7776i 0 28.6145
890.4 3.66638i 0 −9.44232 0.851756i 0 2.76278 19.9536i 0 −3.12286
890.5 3.63886i 0 −9.24130 3.49336i 0 −9.62828 19.0724i 0 −12.7118
890.6 3.62368i 0 −9.13107 3.89223i 0 −8.96960 18.5934i 0 −14.1042
890.7 3.58466i 0 −8.84977 7.20639i 0 4.70987 17.3848i 0 −25.8324
890.8 3.57620i 0 −8.78923 5.13671i 0 4.24305 17.1272i 0 18.3699
890.9 3.22737i 0 −6.41592 1.45400i 0 2.15873 7.79707i 0 4.69259
890.10 3.21080i 0 −6.30922 0.600942i 0 12.4847 7.41443i 0 −1.92950
890.11 3.06240i 0 −5.37827 5.25232i 0 −2.64254 4.22081i 0 −16.0847
890.12 3.03383i 0 −5.20412 9.69466i 0 −0.465658 3.65310i 0 29.4119
890.13 2.99230i 0 −4.95386 7.40706i 0 −4.26180 2.85423i 0 22.1641
890.14 2.96858i 0 −4.81247 3.90126i 0 11.9179 2.41189i 0 11.5812
890.15 2.89430i 0 −4.37696 0.368899i 0 −11.4242 1.09103i 0 1.06770
890.16 2.71611i 0 −3.37726 6.95811i 0 4.31599 1.69142i 0 −18.8990
890.17 2.56806i 0 −2.59492 0.662170i 0 −12.8177 3.60832i 0 1.70049
890.18 2.51986i 0 −2.34969 1.17863i 0 3.92062 4.15855i 0 2.96998
890.19 2.47320i 0 −2.11671 7.47527i 0 −3.57682 4.65775i 0 −18.4878
890.20 2.40991i 0 −1.80767 4.01304i 0 −8.05053 5.28331i 0 9.67106
See all 84 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 890.84
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1143.3.b.a 84
3.b odd 2 1 inner 1143.3.b.a 84
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1143.3.b.a 84 1.a even 1 1 trivial
1143.3.b.a 84 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1143, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database