Properties

Label 1155.3.b.a
Level 1155
Weight 3
Character orbit 1155.b
Analytic conductor 31.471
Analytic rank 0
Dimension 96
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 1155.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.4714705336\)
Analytic rank: \(0\)
Dimension: \(96\)
Coefficient ring index: multiple of None
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.

\(\operatorname{Tr}(f)(q) = \) \( 96q - 216q^{4} + 288q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 96q - 216q^{4} + 288q^{9} + 40q^{11} - 56q^{14} + 488q^{16} + 56q^{22} + 16q^{23} + 480q^{25} - 64q^{26} + 192q^{31} + 24q^{33} + 176q^{34} - 648q^{36} - 112q^{37} - 272q^{38} - 520q^{44} + 416q^{47} - 192q^{48} - 672q^{49} + 112q^{53} - 80q^{55} + 280q^{56} - 352q^{58} + 512q^{59} - 1112q^{64} + 288q^{66} - 304q^{67} - 480q^{71} + 224q^{77} + 240q^{78} + 864q^{81} - 720q^{82} - 432q^{86} - 376q^{88} - 32q^{89} - 384q^{92} + 384q^{93} + 272q^{97} + 120q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
736.1 3.97461i −1.73205 −11.7975 −2.23607 6.88422i 2.64575i 30.9920i 3.00000 8.88749i
736.2 3.80731i −1.73205 −10.4956 −2.23607 6.59446i 2.64575i 24.7309i 3.00000 8.51341i
736.3 3.79404i 1.73205 −10.3948 2.23607 6.57148i 2.64575i 24.2621i 3.00000 8.48374i
736.4 3.73924i 1.73205 −9.98188 −2.23607 6.47655i 2.64575i 22.3677i 3.00000 8.36118i
736.5 3.73084i −1.73205 −9.91918 2.23607 6.46201i 2.64575i 22.0835i 3.00000 8.34242i
736.6 3.67613i 1.73205 −9.51395 −2.23607 6.36725i 2.64575i 20.2700i 3.00000 8.22008i
736.7 3.66479i −1.73205 −9.43072 2.23607 6.34761i 2.64575i 19.9025i 3.00000 8.19473i
736.8 3.64908i 1.73205 −9.31580 2.23607 6.32039i 2.64575i 19.3978i 3.00000 8.15959i
736.9 3.57619i −1.73205 −8.78910 2.23607 6.19413i 2.64575i 17.1267i 3.00000 7.99659i
736.10 3.57202i 1.73205 −8.75932 −2.23607 6.18692i 2.64575i 17.0004i 3.00000 7.98728i
736.11 3.29262i 1.73205 −6.84133 2.23607 5.70298i 2.64575i 9.35542i 3.00000 7.36252i
736.12 3.27785i −1.73205 −6.74433 −2.23607 5.67741i 2.64575i 8.99550i 3.00000 7.32950i
736.13 3.25995i 1.73205 −6.62729 2.23607 5.64640i 2.64575i 8.56486i 3.00000 7.28948i
736.14 2.97479i 1.73205 −4.84935 2.23607 5.15248i 2.64575i 2.52665i 3.00000 6.65182i
736.15 2.94196i 1.73205 −4.65512 −2.23607 5.09562i 2.64575i 1.92733i 3.00000 6.57842i
736.16 2.91962i −1.73205 −4.52416 2.23607 5.05692i 2.64575i 1.53034i 3.00000 6.52846i
736.17 2.91387i −1.73205 −4.49063 2.23607 5.04697i 2.64575i 1.42964i 3.00000 6.51561i
736.18 2.89693i −1.73205 −4.39221 2.23607 5.01763i 2.64575i 1.13621i 3.00000 6.47774i
736.19 2.81721i −1.73205 −3.93666 −2.23607 4.87955i 2.64575i 0.178435i 3.00000 6.29947i
736.20 2.77171i −1.73205 −3.68240 −2.23607 4.80075i 2.64575i 0.880291i 3.00000 6.19774i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 736.96
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1155.3.b.a 96
11.b odd 2 1 inner 1155.3.b.a 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.3.b.a 96 1.a even 1 1 trivial
1155.3.b.a 96 11.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1155, [\chi])\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database