Properties

Label 8015.2.a.i
Level 8015
Weight 2
Character orbit 8015.a
Self dual Yes
Analytic conductor 64.000
Analytic rank 1
Dimension 44
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(1\)
Dimension: \(44\)
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.

\(\operatorname{Tr}(f)(q) = \) \(44q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut +\mathstrut 44q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 44q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(44q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut +\mathstrut 44q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 44q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 15q^{11} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut -\mathstrut 17q^{13} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 10q^{16} \) \(\mathstrut -\mathstrut 7q^{17} \) \(\mathstrut -\mathstrut 16q^{18} \) \(\mathstrut -\mathstrut 32q^{19} \) \(\mathstrut +\mathstrut 30q^{20} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 35q^{24} \) \(\mathstrut +\mathstrut 44q^{25} \) \(\mathstrut -\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 6q^{27} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 7q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut -\mathstrut 8q^{32} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 33q^{34} \) \(\mathstrut -\mathstrut 44q^{35} \) \(\mathstrut -\mathstrut 11q^{36} \) \(\mathstrut -\mathstrut 44q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 62q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 7q^{43} \) \(\mathstrut -\mathstrut 45q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 26q^{48} \) \(\mathstrut +\mathstrut 44q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 25q^{51} \) \(\mathstrut -\mathstrut 35q^{52} \) \(\mathstrut -\mathstrut 25q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut +\mathstrut 3q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 35q^{59} \) \(\mathstrut -\mathstrut 3q^{60} \) \(\mathstrut -\mathstrut 86q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 5q^{64} \) \(\mathstrut -\mathstrut 17q^{65} \) \(\mathstrut -\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 2q^{67} \) \(\mathstrut -\mathstrut q^{68} \) \(\mathstrut -\mathstrut 75q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 54q^{71} \) \(\mathstrut -\mathstrut 3q^{72} \) \(\mathstrut -\mathstrut 52q^{73} \) \(\mathstrut -\mathstrut 22q^{74} \) \(\mathstrut -\mathstrut 77q^{76} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 72q^{81} \) \(\mathstrut -\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 3q^{84} \) \(\mathstrut -\mathstrut 7q^{85} \) \(\mathstrut -\mathstrut 33q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 23q^{88} \) \(\mathstrut -\mathstrut 105q^{89} \) \(\mathstrut -\mathstrut 16q^{90} \) \(\mathstrut +\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 41q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut -\mathstrut 47q^{94} \) \(\mathstrut -\mathstrut 32q^{95} \) \(\mathstrut -\mathstrut 39q^{96} \) \(\mathstrut -\mathstrut 80q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 53q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.79746 −0.603519 5.82580 1.00000 1.68832 −1.00000 −10.7025 −2.63576 −2.79746
1.2 −2.53948 2.62786 4.44894 1.00000 −6.67339 −1.00000 −6.21901 3.90566 −2.53948
1.3 −2.32161 −1.61048 3.38989 1.00000 3.73891 −1.00000 −3.22677 −0.406353 −2.32161
1.4 −2.27226 −1.26810 3.16315 1.00000 2.88144 −1.00000 −2.64298 −1.39193 −2.27226
1.5 −2.26027 2.68549 3.10882 1.00000 −6.06994 −1.00000 −2.50623 4.21188 −2.26027
1.6 −2.24100 −0.455413 3.02210 1.00000 1.02058 −1.00000 −2.29052 −2.79260 −2.24100
1.7 −2.23576 0.480979 2.99861 1.00000 −1.07535 −1.00000 −2.23266 −2.76866 −2.23576
1.8 −1.87978 3.08968 1.53356 1.00000 −5.80791 −1.00000 0.876807 6.54615 −1.87978
1.9 −1.84251 −2.60277 1.39485 1.00000 4.79563 −1.00000 1.11499 3.77440 −1.84251
1.10 −1.65863 1.21505 0.751045 1.00000 −2.01532 −1.00000 2.07155 −1.52365 −1.65863
1.11 −1.54745 −2.71325 0.394610 1.00000 4.19863 −1.00000 2.48426 4.36174 −1.54745
1.12 −1.41331 0.0185355 −0.00254977 1.00000 −0.0261965 −1.00000 2.83023 −2.99966 −1.41331
1.13 −1.25477 1.22958 −0.425541 1.00000 −1.54284 −1.00000 3.04351 −1.48814 −1.25477
1.14 −1.22585 2.00155 −0.497288 1.00000 −2.45360 −1.00000 3.06130 1.00619 −1.22585
1.15 −1.22552 −2.22296 −0.498095 1.00000 2.72428 −1.00000 3.06147 1.94153 −1.22552
1.16 −1.03648 −2.16444 −0.925705 1.00000 2.24341 −1.00000 3.03244 1.68482 −1.03648
1.17 −0.631186 1.05743 −1.60160 1.00000 −0.667437 −1.00000 2.27328 −1.88184 −0.631186
1.18 −0.612476 −1.57448 −1.62487 1.00000 0.964330 −1.00000 2.22015 −0.521024 −0.612476
1.19 −0.583301 −0.502435 −1.65976 1.00000 0.293071 −1.00000 2.13474 −2.74756 −0.583301
1.20 −0.508100 2.08594 −1.74183 1.00000 −1.05987 −1.00000 1.90123 1.35113 −0.508100
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.44
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(1\)
\(229\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

\(T_{2}^{44} + \cdots\)
\(T_{3}^{44} - \cdots\)