Properties

Label 4015.2.a.c
Level 4015
Weight 2
Character orbit 4015.a
Self dual Yes
Analytic conductor 32.060
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 23q - 3q^{2} - 5q^{3} + 15q^{4} + 23q^{5} - 5q^{6} - 6q^{8} + 8q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 23q - 3q^{2} - 5q^{3} + 15q^{4} + 23q^{5} - 5q^{6} - 6q^{8} + 8q^{9} - 3q^{10} - 23q^{11} - 18q^{12} - 5q^{13} - 17q^{14} - 5q^{15} - q^{16} - 36q^{17} + q^{18} + 6q^{19} + 15q^{20} - 18q^{21} + 3q^{22} - 14q^{23} - 7q^{24} + 23q^{25} - 21q^{26} - 29q^{27} + 28q^{28} - 36q^{29} - 5q^{30} - 16q^{31} - 5q^{32} + 5q^{33} - 28q^{34} - 14q^{36} - 24q^{37} + q^{38} - 10q^{39} - 6q^{40} - 36q^{41} - 5q^{42} + 17q^{43} - 15q^{44} + 8q^{45} - 25q^{46} - 21q^{47} - 17q^{48} - 27q^{49} - 3q^{50} + 19q^{51} - 21q^{52} - 28q^{53} - 15q^{54} - 23q^{55} - 46q^{56} - 23q^{57} - 16q^{58} - 61q^{59} - 18q^{60} - 17q^{61} - 22q^{62} - 9q^{63} - 18q^{64} - 5q^{65} + 5q^{66} + 2q^{67} - 39q^{68} - 36q^{69} - 17q^{70} - 50q^{71} + 15q^{72} + 23q^{73} + 17q^{74} - 5q^{75} - 21q^{76} + 49q^{78} - 18q^{79} - q^{80} - 57q^{81} + 14q^{82} - 20q^{83} - 38q^{84} - 36q^{85} - 45q^{86} + 37q^{87} + 6q^{88} - 93q^{89} + q^{90} - 42q^{91} - 39q^{92} - 18q^{93} - 6q^{94} + 6q^{95} - 9q^{96} - 31q^{97} - 31q^{98} - 8q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.63381 −0.811587 4.93698 1.00000 2.13757 5.26915 −7.73545 −2.34133 −2.63381
1.2 −2.41301 1.23805 3.82260 1.00000 −2.98742 −1.94006 −4.39795 −1.46724 −2.41301
1.3 −2.26107 −2.17834 3.11244 1.00000 4.92537 1.01936 −2.51531 1.74515 −2.26107
1.4 −2.15888 1.54599 2.66074 1.00000 −3.33759 2.48210 −1.42646 −0.609922 −2.15888
1.5 −2.00725 −2.63655 2.02904 1.00000 5.29220 −1.13661 −0.0582891 3.95138 −2.00725
1.6 −1.63550 2.32797 0.674867 1.00000 −3.80740 −0.601850 2.16726 2.41945 −1.63550
1.7 −1.22952 −0.451066 −0.488282 1.00000 0.554594 −2.48868 3.05939 −2.79654 −1.22952
1.8 −1.17870 −1.42513 −0.610675 1.00000 1.67979 3.29739 3.07719 −0.969018 −1.17870
1.9 −0.975417 1.70884 −1.04856 1.00000 −1.66683 0.984932 2.97362 −0.0798559 −0.975417
1.10 −0.760826 0.764917 −1.42114 1.00000 −0.581969 −2.66383 2.60290 −2.41490 −0.760826
1.11 −0.692372 −2.63531 −1.52062 1.00000 1.82461 0.337135 2.43758 3.94484 −0.692372
1.12 −0.197331 2.44280 −1.96106 1.00000 −0.482041 −1.78119 0.781640 2.96728 −0.197331
1.13 0.418197 2.15176 −1.82511 1.00000 0.899862 0.524806 −1.59965 1.63009 0.418197
1.14 0.422103 −2.19245 −1.82183 1.00000 −0.925438 −3.51396 −1.61321 1.80682 0.422103
1.15 0.615983 −0.785692 −1.62056 1.00000 −0.483973 2.63763 −2.23021 −2.38269 0.615983
1.16 0.661798 −2.32231 −1.56202 1.00000 −1.53690 −0.917277 −2.35734 2.39311 0.661798
1.17 1.20516 1.14152 −0.547593 1.00000 1.37572 3.42329 −3.07025 −1.69692 1.20516
1.18 1.30572 1.83317 −0.295101 1.00000 2.39360 −4.41824 −2.99675 0.360505 1.30572
1.19 1.83759 −0.530531 1.37674 1.00000 −0.974898 1.03293 −1.14530 −2.71854 1.83759
1.20 1.92108 −3.32354 1.69056 1.00000 −6.38479 2.35268 −0.594467 8.04590 1.92108
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
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Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(11\) \(1\)
\(73\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{23} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\).