Properties

Label 1183.2.e.j
Level $1183$
Weight $2$
Character orbit 1183.e
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} - 24q^{10} + 2q^{12} + 8q^{14} - 16q^{16} - 34q^{17} + 60q^{22} - 6q^{23} + 10q^{25} + 24q^{27} + 4q^{29} - 22q^{30} - 24q^{35} - 52q^{36} - 38q^{38} - 2q^{40} + 32q^{42} + 44q^{43} - 76q^{48} + 12q^{49} - 8q^{51} - 16q^{53} + 60q^{55} + 54q^{56} + 10q^{61} + 164q^{62} - 4q^{64} - 68q^{66} - 22q^{68} + 28q^{69} - 66q^{74} - 2q^{75} + 38q^{77} - 70q^{79} + 28q^{81} - 10q^{82} + 20q^{87} + 28q^{88} - 132q^{92} + 2q^{94} - 4q^{95} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
170.1 −1.29430 + 2.24179i −0.259233 0.449005i −2.35043 4.07106i −0.806027 + 1.39608i 1.34210 2.13104 + 1.56802i 6.99143 1.36560 2.36528i −2.08648 3.61389i
170.2 −1.15163 + 1.99469i 0.736680 + 1.27597i −1.65252 2.86225i −0.423646 + 0.733776i −3.39354 −1.00088 2.44913i 3.00585 0.414604 0.718115i −0.975769 1.69008i
170.3 −0.689527 + 1.19430i −1.44060 2.49520i 0.0491037 + 0.0850501i −0.402974 + 0.697972i 3.97334 −1.26180 2.32548i −2.89354 −2.65067 + 4.59109i −0.555723 0.962541i
170.4 −0.672613 + 1.16500i −1.02505 1.77544i 0.0951832 + 0.164862i −1.78389 + 3.08979i 2.75785 2.62255 0.349630i −2.94654 −0.601462 + 1.04176i −2.39973 4.15646i
170.5 −0.249993 + 0.433001i −0.424801 0.735776i 0.875007 + 1.51556i 0.521238 0.902810i 0.424789 −2.40155 + 1.11021i −1.87496 1.13909 1.97296i 0.260612 + 0.451393i
170.6 −0.0904119 + 0.156598i 0.913006 + 1.58137i 0.983651 + 1.70373i −1.34332 + 2.32670i −0.330186 −1.64912 + 2.06892i −0.717383 −0.167162 + 0.289532i −0.242904 0.420723i
170.7 0.0904119 0.156598i 0.913006 + 1.58137i 0.983651 + 1.70373i 1.34332 2.32670i 0.330186 1.64912 2.06892i 0.717383 −0.167162 + 0.289532i −0.242904 0.420723i
170.8 0.249993 0.433001i −0.424801 0.735776i 0.875007 + 1.51556i −0.521238 + 0.902810i −0.424789 2.40155 1.11021i 1.87496 1.13909 1.97296i 0.260612 + 0.451393i
170.9 0.672613 1.16500i −1.02505 1.77544i 0.0951832 + 0.164862i 1.78389 3.08979i −2.75785 −2.62255 + 0.349630i 2.94654 −0.601462 + 1.04176i −2.39973 4.15646i
170.10 0.689527 1.19430i −1.44060 2.49520i 0.0491037 + 0.0850501i 0.402974 0.697972i −3.97334 1.26180 + 2.32548i 2.89354 −2.65067 + 4.59109i −0.555723 0.962541i
170.11 1.15163 1.99469i 0.736680 + 1.27597i −1.65252 2.86225i 0.423646 0.733776i 3.39354 1.00088 + 2.44913i −3.00585 0.414604 0.718115i −0.975769 1.69008i
170.12 1.29430 2.24179i −0.259233 0.449005i −2.35043 4.07106i 0.806027 1.39608i −1.34210 −2.13104 1.56802i −6.99143 1.36560 2.36528i −2.08648 3.61389i
508.1 −1.29430 2.24179i −0.259233 + 0.449005i −2.35043 + 4.07106i −0.806027 1.39608i 1.34210 2.13104 1.56802i 6.99143 1.36560 + 2.36528i −2.08648 + 3.61389i
508.2 −1.15163 1.99469i 0.736680 1.27597i −1.65252 + 2.86225i −0.423646 0.733776i −3.39354 −1.00088 + 2.44913i 3.00585 0.414604 + 0.718115i −0.975769 + 1.69008i
508.3 −0.689527 1.19430i −1.44060 + 2.49520i 0.0491037 0.0850501i −0.402974 0.697972i 3.97334 −1.26180 + 2.32548i −2.89354 −2.65067 4.59109i −0.555723 + 0.962541i
508.4 −0.672613 1.16500i −1.02505 + 1.77544i 0.0951832 0.164862i −1.78389 3.08979i 2.75785 2.62255 + 0.349630i −2.94654 −0.601462 1.04176i −2.39973 + 4.15646i
508.5 −0.249993 0.433001i −0.424801 + 0.735776i 0.875007 1.51556i 0.521238 + 0.902810i 0.424789 −2.40155 1.11021i −1.87496 1.13909 + 1.97296i 0.260612 0.451393i
508.6 −0.0904119 0.156598i 0.913006 1.58137i 0.983651 1.70373i −1.34332 2.32670i −0.330186 −1.64912 2.06892i −0.717383 −0.167162 0.289532i −0.242904 + 0.420723i
508.7 0.0904119 + 0.156598i 0.913006 1.58137i 0.983651 1.70373i 1.34332 + 2.32670i 0.330186 1.64912 + 2.06892i 0.717383 −0.167162 0.289532i −0.242904 + 0.420723i
508.8 0.249993 + 0.433001i −0.424801 + 0.735776i 0.875007 1.51556i −0.521238 0.902810i −0.424789 2.40155 + 1.11021i 1.87496 1.13909 + 1.97296i 0.260612 0.451393i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 508.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner
13.b even 2 1 inner
91.r even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1183.2.e.j 24
7.c even 3 1 inner 1183.2.e.j 24
7.c even 3 1 8281.2.a.cp 12
7.d odd 6 1 8281.2.a.co 12
13.b even 2 1 inner 1183.2.e.j 24
13.f odd 12 1 91.2.k.b 12
13.f odd 12 1 91.2.u.b yes 12
39.k even 12 1 819.2.bm.f 12
39.k even 12 1 819.2.do.e 12
91.r even 6 1 inner 1183.2.e.j 24
91.r even 6 1 8281.2.a.cp 12
91.s odd 6 1 8281.2.a.co 12
91.w even 12 1 637.2.k.i 12
91.w even 12 1 637.2.q.i 12
91.x odd 12 1 91.2.u.b yes 12
91.x odd 12 1 637.2.q.g 12
91.ba even 12 1 637.2.q.i 12
91.ba even 12 1 637.2.u.g 12
91.bc even 12 1 637.2.k.i 12
91.bc even 12 1 637.2.u.g 12
91.bd odd 12 1 91.2.k.b 12
91.bd odd 12 1 637.2.q.g 12
273.bv even 12 1 819.2.do.e 12
273.bw even 12 1 819.2.bm.f 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
91.2.k.b 12 13.f odd 12 1
91.2.k.b 12 91.bd odd 12 1
91.2.u.b yes 12 13.f odd 12 1
91.2.u.b yes 12 91.x odd 12 1
637.2.k.i 12 91.w even 12 1
637.2.k.i 12 91.bc even 12 1
637.2.q.g 12 91.x odd 12 1
637.2.q.g 12 91.bd odd 12 1
637.2.q.i 12 91.w even 12 1
637.2.q.i 12 91.ba even 12 1
637.2.u.g 12 91.ba even 12 1
637.2.u.g 12 91.bc even 12 1
819.2.bm.f 12 39.k even 12 1
819.2.bm.f 12 273.bw even 12 1
819.2.do.e 12 39.k even 12 1
819.2.do.e 12 273.bv even 12 1
1183.2.e.j 24 1.a even 1 1 trivial
1183.2.e.j 24 7.c even 3 1 inner
1183.2.e.j 24 13.b even 2 1 inner
1183.2.e.j 24 91.r even 6 1 inner
8281.2.a.co 12 7.d odd 6 1
8281.2.a.co 12 91.s odd 6 1
8281.2.a.cp 12 7.c even 3 1
8281.2.a.cp 12 91.r even 6 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1183, [\chi])\):

\(T_{2}^{24} + \cdots\)
\(T_{3}^{12} + \cdots\)