Properties

Label 43.11.b.b
Level 43
Weight 11
Character orbit 43.b
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 43 \)
Weight: \( k \) = \( 11 \)
Character orbit: \([\chi]\) = 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(34\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
42.1 59.1014i 419.853i −2468.98 832.528i 24813.9 31219.1i 85400.1i −117228. −49203.6
42.2 58.7853i 301.513i −2431.72 2781.13i −17724.6 4095.06i 82753.1i −31861.2 −163489.
42.3 57.1045i 18.6474i −2236.92 2202.14i 1064.85 1818.95i 69263.1i 58701.3 125752.
42.4 50.9791i 197.849i −1574.87 5530.45i 10086.2 21393.6i 28082.7i 19904.8 −281938.
42.5 46.2007i 372.330i −1110.50 2517.50i 17201.9 25292.2i 3996.58i −79580.9 116310.
42.6 44.1717i 389.187i −927.142 5234.98i −17191.1 21894.1i 4278.39i −92417.4 231238.
42.7 43.4520i 375.725i −864.079 561.891i −16326.0 26275.3i 6948.90i −82120.5 −24415.3
42.8 41.3871i 57.8259i −688.891 4608.97i 2393.24 16533.3i 13869.2i 55705.2 −190752.
42.9 41.1797i 18.8325i −671.767 4211.22i −775.516 20378.0i 14504.9i 58694.3 173417.
42.10 30.3109i 212.897i 105.247 1632.05i −6453.11 7423.10i 34228.5i 13723.9 −49468.9
42.11 29.9454i 271.957i 127.271 203.516i 8143.86 3479.85i 34475.3i −14911.3 −6094.37
42.12 24.5024i 131.608i 423.632 1067.29i −3224.72 23187.4i 35470.5i 41728.3 −26151.2
42.13 21.4666i 198.865i 563.184 4591.08i 4268.96 9954.72i 34071.5i 19501.8 98554.8
42.14 16.6799i 405.855i 745.782 2509.28i 6769.61 11110.8i 29519.7i −105670. −41854.4
42.15 10.4458i 477.424i 914.885 5026.78i −4987.08 7308.14i 20253.2i −168885. −52508.8
42.16 5.51570i 292.852i 993.577 3204.10i −1615.28 16511.8i 11128.3i −26713.4 17672.9
42.17 0.846054i 54.5873i 1023.28 4881.88i −46.1839 30624.2i 1732.11i 56069.2 −4130.34
42.18 0.846054i 54.5873i 1023.28 4881.88i −46.1839 30624.2i 1732.11i 56069.2 −4130.34
42.19 5.51570i 292.852i 993.577 3204.10i −1615.28 16511.8i 11128.3i −26713.4 17672.9
42.20 10.4458i 477.424i 914.885 5026.78i −4987.08 7308.14i 20253.2i −168885. −52508.8
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 42.34
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 43.11.b.b 34
43.b odd 2 1 inner 43.11.b.b 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.11.b.b 34 1.a even 1 1 trivial
43.11.b.b 34 43.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{34} + \cdots\) acting on \(S_{11}^{\mathrm{new}}(43, [\chi])\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database