Properties

Label 1148.2.ba.a
Level $1148$
Weight $2$
Character orbit 1148.ba
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
113.1 0 3.08866i 0 −1.11364 3.42744i 0 −0.587785 0.809017i 0 −6.53981 0
113.2 0 2.81622i 0 1.10836 + 3.41119i 0 0.587785 + 0.809017i 0 −4.93108 0
113.3 0 2.47691i 0 0.848862 + 2.61253i 0 −0.587785 0.809017i 0 −3.13508 0
113.4 0 2.09016i 0 −0.164331 0.505760i 0 0.587785 + 0.809017i 0 −1.36876 0
113.5 0 1.92602i 0 −0.139283 0.428669i 0 0.587785 + 0.809017i 0 −0.709536 0
113.6 0 1.80180i 0 −0.0346732 0.106713i 0 −0.587785 0.809017i 0 −0.246466 0
113.7 0 1.15530i 0 −1.04872 3.22763i 0 −0.587785 0.809017i 0 1.66528 0
113.8 0 0.904348i 0 0.129544 + 0.398696i 0 −0.587785 0.809017i 0 2.18215 0
113.9 0 0.216695i 0 −1.22916 3.78295i 0 0.587785 + 0.809017i 0 2.95304 0
113.10 0 0.268055i 0 0.725265 + 2.23214i 0 0.587785 + 0.809017i 0 2.92815 0
113.11 0 0.304900i 0 −0.420940 1.29552i 0 0.587785 + 0.809017i 0 2.90704 0
113.12 0 0.927936i 0 0.718305 + 2.21072i 0 −0.587785 0.809017i 0 2.13894 0
113.13 0 1.06924i 0 0.727989 + 2.24052i 0 −0.587785 0.809017i 0 1.85672 0
113.14 0 1.48167i 0 −0.0508728 0.156570i 0 0.587785 + 0.809017i 0 0.804648 0
113.15 0 1.49455i 0 −0.331199 1.01933i 0 −0.587785 0.809017i 0 0.766322 0
113.16 0 2.20495i 0 0.330069 + 1.01585i 0 −0.587785 0.809017i 0 −1.86181 0
113.17 0 2.28455i 0 1.15282 + 3.54801i 0 0.587785 + 0.809017i 0 −2.21915 0
113.18 0 2.48140i 0 −0.290583 0.894324i 0 0.587785 + 0.809017i 0 −3.15734 0
113.19 0 2.90590i 0 −0.726535 2.23605i 0 −0.587785 0.809017i 0 −5.44428 0
113.20 0 2.97070i 0 −1.19128 3.66638i 0 0.587785 + 0.809017i 0 −5.82504 0
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1009.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
41.f even 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1148.2.ba.a 80
41.f even 10 1 inner 1148.2.ba.a 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1148.2.ba.a 80 1.a even 1 1 trivial
1148.2.ba.a 80 41.f even 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1148, [\chi])\).