Properties

Label 91.8.c.a
Level $91$
Weight $8$
Character orbit 91.c
Analytic conductor $28.427$
Analytic rank $0$
Dimension $50$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.4270373191\)
Analytic rank: \(0\)
Dimension: \(50\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 50 q - 3328 q^{4} + 40514 q^{9} + 5320 q^{10} + 8700 q^{12} + 17044 q^{13} + 10976 q^{14} + 228808 q^{16} + 33664 q^{17} + 70228 q^{22} - 75042 q^{23} - 664772 q^{25} + 78276 q^{26} - 661404 q^{27} + 135778 q^{29} + 994888 q^{30} + 372498 q^{35} - 3549604 q^{36} + 338468 q^{38} - 973080 q^{39} + 79316 q^{40} + 296352 q^{42} - 53618 q^{43} + 1400384 q^{48} - 5882450 q^{49} - 2182360 q^{51} - 6982340 q^{52} + 2841746 q^{53} + 6871356 q^{55} - 2107392 q^{56} + 1773716 q^{61} - 6969608 q^{62} - 9449120 q^{64} - 7901430 q^{65} - 11755548 q^{66} + 11829980 q^{68} + 3564460 q^{69} + 45595884 q^{74} - 7220964 q^{75} + 186592 q^{77} - 8093012 q^{78} - 21257822 q^{79} + 53034530 q^{81} + 10907568 q^{82} + 14135000 q^{87} - 51594780 q^{88} - 61226356 q^{90} - 8096858 q^{91} - 11200212 q^{92} + 80667028 q^{94} + 30430066 q^{95}+O(q^{100}) \) Copy content Toggle raw display

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
64.1 22.2828i −16.8313 −368.522 186.348i 375.049i 343.000i 5359.48i −1903.71 4152.34
64.2 21.0014i 55.1097 −313.061 298.534i 1157.38i 343.000i 3886.54i 850.082 6269.64
64.3 20.4516i −67.6652 −290.269 268.414i 1383.86i 343.000i 3318.67i 2391.58 5489.50
64.4 20.3011i 50.0015 −284.134 340.641i 1015.08i 343.000i 3169.69i 313.148 −6915.39
64.5 20.0790i −84.8054 −275.166 538.452i 1702.81i 343.000i 2954.94i 5004.96 −10811.6
64.6 19.2961i 46.7043 −244.338 300.001i 901.208i 343.000i 2244.87i −5.71295 −5788.83
64.7 17.7532i −30.0870 −187.174 248.659i 534.138i 343.000i 1050.53i −1281.77 −4414.48
64.8 16.9891i 92.8773 −160.631 107.578i 1577.91i 343.000i 554.371i 6439.20 1827.67
64.9 15.7347i 36.7387 −119.582 452.285i 578.073i 343.000i 132.453i −837.271 7116.58
64.10 15.4646i −2.30214 −111.152 85.0277i 35.6015i 343.000i 260.539i −2181.70 1314.92
64.11 15.1105i 24.8832 −100.328 394.355i 375.998i 343.000i 418.137i −1567.83 5958.92
64.12 14.7173i −70.7615 −88.5983 406.740i 1041.42i 343.000i 579.886i 2820.20 5986.11
64.13 12.6128i −83.1101 −31.0818 6.92246i 1048.25i 343.000i 1222.41i 4720.29 87.3113
64.14 11.3642i 31.8809 −1.14421 405.714i 362.299i 343.000i 1441.61i −1170.61 −4610.60
64.15 11.0195i −52.4283 6.57091 215.435i 577.733i 343.000i 1482.90i 561.727 −2373.98
64.16 10.6365i 74.1121 14.8657 114.172i 788.291i 343.000i 1519.59i 3305.61 −1214.39
64.17 9.69261i −28.8717 34.0534 266.481i 279.842i 343.000i 1570.72i −1353.43 2582.90
64.18 8.36017i −8.01801 58.1075 455.948i 67.0319i 343.000i 1555.89i −2122.71 −3811.80
64.19 5.70969i −8.30892 95.3995 279.609i 47.4413i 343.000i 1275.54i −2117.96 1596.48
64.20 4.39578i −84.2461 108.677 187.956i 370.327i 343.000i 1040.38i 4910.40 −826.214
See all 50 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 64.50
Significant digits:
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Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 91.8.c.a 50
13.b even 2 1 inner 91.8.c.a 50
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
91.8.c.a 50 1.a even 1 1 trivial
91.8.c.a 50 13.b even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{8}^{\mathrm{new}}(91, [\chi])\).