Properties

Label 15.8.e.a
Level 15
Weight 8
Character orbit 15.e
Analytic conductor 4.686
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 15.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(4.68577538226\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24q + 24q^{3} + 924q^{6} + 1344q^{7} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q + 24q^{3} + 924q^{6} + 1344q^{7} - 3180q^{10} - 2028q^{12} + 16848q^{13} + 37560q^{15} - 68868q^{16} - 106560q^{18} + 84144q^{21} + 166020q^{22} - 275760q^{25} - 264168q^{27} + 602028q^{28} + 892380q^{30} - 208992q^{31} - 877800q^{33} - 256212q^{36} - 635616q^{37} - 1574040q^{40} + 1219380q^{42} + 1397328q^{43} + 570240q^{45} + 2787168q^{46} - 476796q^{48} - 4028016q^{51} - 6426336q^{52} + 2324880q^{55} + 8457264q^{57} + 986340q^{58} + 2037900q^{60} + 12157968q^{61} - 1973952q^{63} - 25406040q^{66} - 16720176q^{67} - 13165860q^{70} + 36245880q^{72} + 4059528q^{73} + 11226120q^{75} + 37968816q^{76} - 26156280q^{78} - 31289976q^{81} - 53633520q^{82} - 34181760q^{85} + 44480160q^{87} + 74717340q^{88} + 71623080q^{90} + 67599648q^{91} - 58742592q^{93} - 103105308q^{96} - 75148056q^{97} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −14.4708 + 14.4708i −45.2107 11.9578i 290.808i −140.740 + 241.490i 827.274 481.197i 196.040 + 196.040i 2355.96 + 2355.96i 1901.02 + 1081.24i −1457.93 5531.17i
2.2 −13.2671 + 13.2671i 42.4163 19.6942i 224.030i 122.889 251.044i −301.455 + 824.023i 796.332 + 796.332i 1274.03 + 1274.03i 1411.28 1670.71i 1700.24 + 4961.00i
2.3 −9.36735 + 9.36735i 23.6872 + 40.3227i 47.4943i 125.932 + 249.532i −599.602 155.830i −696.811 696.811i −754.124 754.124i −1064.84 + 1910.26i −3517.10 1157.80i
2.4 −6.70096 + 6.70096i −34.4749 + 31.5988i 38.1944i 8.44382 279.381i 19.2725 442.757i −68.7247 68.7247i −1113.66 1113.66i 190.033 2178.73i 1815.54 + 1928.70i
2.5 −5.42850 + 5.42850i 13.1156 44.8885i 69.0629i −275.850 + 45.0737i 172.479 + 314.875i −775.470 775.470i −1069.75 1069.75i −1842.96 1177.48i 1252.77 1742.13i
2.6 −1.72123 + 1.72123i −28.9107 36.7583i 122.075i 270.133 + 71.7849i 113.031 + 13.5074i 884.635 + 884.635i −430.436 430.436i −515.339 + 2125.42i −588.519 + 341.403i
2.7 1.72123 1.72123i 36.7583 + 28.9107i 122.075i −270.133 71.7849i 113.031 13.5074i 884.635 + 884.635i 430.436 + 430.436i 515.339 + 2125.42i −588.519 + 341.403i
2.8 5.42850 5.42850i 44.8885 13.1156i 69.0629i 275.850 45.0737i 172.479 314.875i −775.470 775.470i 1069.75 + 1069.75i 1842.96 1177.48i 1252.77 1742.13i
2.9 6.70096 6.70096i −31.5988 + 34.4749i 38.1944i −8.44382 + 279.381i 19.2725 + 442.757i −68.7247 68.7247i 1113.66 + 1113.66i −190.033 2178.73i 1815.54 + 1928.70i
2.10 9.36735 9.36735i −40.3227 23.6872i 47.4943i −125.932 249.532i −599.602 + 155.830i −696.811 696.811i 754.124 + 754.124i 1064.84 + 1910.26i −3517.10 1157.80i
2.11 13.2671 13.2671i 19.6942 42.4163i 224.030i −122.889 + 251.044i −301.455 824.023i 796.332 + 796.332i −1274.03 1274.03i −1411.28 1670.71i 1700.24 + 4961.00i
2.12 14.4708 14.4708i 11.9578 + 45.2107i 290.808i 140.740 241.490i 827.274 + 481.197i 196.040 + 196.040i −2355.96 2355.96i −1901.02 + 1081.24i −1457.93 5531.17i
8.1 −14.4708 14.4708i −45.2107 + 11.9578i 290.808i −140.740 241.490i 827.274 + 481.197i 196.040 196.040i 2355.96 2355.96i 1901.02 1081.24i −1457.93 + 5531.17i
8.2 −13.2671 13.2671i 42.4163 + 19.6942i 224.030i 122.889 + 251.044i −301.455 824.023i 796.332 796.332i 1274.03 1274.03i 1411.28 + 1670.71i 1700.24 4961.00i
8.3 −9.36735 9.36735i 23.6872 40.3227i 47.4943i 125.932 249.532i −599.602 + 155.830i −696.811 + 696.811i −754.124 + 754.124i −1064.84 1910.26i −3517.10 + 1157.80i
8.4 −6.70096 6.70096i −34.4749 31.5988i 38.1944i 8.44382 + 279.381i 19.2725 + 442.757i −68.7247 + 68.7247i −1113.66 + 1113.66i 190.033 + 2178.73i 1815.54 1928.70i
8.5 −5.42850 5.42850i 13.1156 + 44.8885i 69.0629i −275.850 45.0737i 172.479 314.875i −775.470 + 775.470i −1069.75 + 1069.75i −1842.96 + 1177.48i 1252.77 + 1742.13i
8.6 −1.72123 1.72123i −28.9107 + 36.7583i 122.075i 270.133 71.7849i 113.031 13.5074i 884.635 884.635i −430.436 + 430.436i −515.339 2125.42i −588.519 341.403i
8.7 1.72123 + 1.72123i 36.7583 28.9107i 122.075i −270.133 + 71.7849i 113.031 + 13.5074i 884.635 884.635i 430.436 430.436i 515.339 2125.42i −588.519 341.403i
8.8 5.42850 + 5.42850i 44.8885 + 13.1156i 69.0629i 275.850 + 45.0737i 172.479 + 314.875i −775.470 + 775.470i 1069.75 1069.75i 1842.96 + 1177.48i 1252.77 + 1742.13i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 8.12
Significant digits:
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Inner twists

This newform does not have CM; other inner twists have not been computed.

Hecke kernels

There are no other newforms in \(S_{8}^{\mathrm{new}}(15, [\chi])\).