Properties

Label 8035.2.a.c
Level 8035
Weight 2
Character orbit 8035.a
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 127
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(127\)
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.

\(\operatorname{Tr}(f)(q) = \) \(127q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 125q^{4} \) \(\mathstrut -\mathstrut 127q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut +\mathstrut 54q^{8} \) \(\mathstrut +\mathstrut 123q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(127q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 125q^{4} \) \(\mathstrut -\mathstrut 127q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut +\mathstrut 54q^{8} \) \(\mathstrut +\mathstrut 123q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut +\mathstrut 30q^{11} \) \(\mathstrut +\mathstrut 35q^{12} \) \(\mathstrut +\mathstrut 30q^{13} \) \(\mathstrut +\mathstrut 39q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 121q^{16} \) \(\mathstrut +\mathstrut 63q^{17} \) \(\mathstrut +\mathstrut 53q^{18} \) \(\mathstrut -\mathstrut 35q^{19} \) \(\mathstrut -\mathstrut 125q^{20} \) \(\mathstrut +\mathstrut 33q^{21} \) \(\mathstrut +\mathstrut 49q^{22} \) \(\mathstrut +\mathstrut 61q^{23} \) \(\mathstrut -\mathstrut 5q^{24} \) \(\mathstrut +\mathstrut 127q^{25} \) \(\mathstrut +\mathstrut 10q^{26} \) \(\mathstrut +\mathstrut 40q^{27} \) \(\mathstrut +\mathstrut 32q^{28} \) \(\mathstrut +\mathstrut 134q^{29} \) \(\mathstrut -\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 122q^{32} \) \(\mathstrut +\mathstrut 48q^{33} \) \(\mathstrut -\mathstrut 21q^{34} \) \(\mathstrut -\mathstrut 13q^{35} \) \(\mathstrut +\mathstrut 133q^{36} \) \(\mathstrut +\mathstrut 60q^{37} \) \(\mathstrut +\mathstrut 33q^{38} \) \(\mathstrut +\mathstrut 26q^{39} \) \(\mathstrut -\mathstrut 54q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 45q^{42} \) \(\mathstrut +\mathstrut 48q^{43} \) \(\mathstrut +\mathstrut 85q^{44} \) \(\mathstrut -\mathstrut 123q^{45} \) \(\mathstrut -\mathstrut 11q^{46} \) \(\mathstrut +\mathstrut 57q^{47} \) \(\mathstrut +\mathstrut 71q^{48} \) \(\mathstrut +\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 45q^{51} \) \(\mathstrut +\mathstrut 68q^{52} \) \(\mathstrut +\mathstrut 182q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut +\mathstrut 96q^{56} \) \(\mathstrut +\mathstrut 74q^{57} \) \(\mathstrut +\mathstrut 47q^{58} \) \(\mathstrut +\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 35q^{60} \) \(\mathstrut +\mathstrut 16q^{61} \) \(\mathstrut +\mathstrut 43q^{62} \) \(\mathstrut +\mathstrut 73q^{63} \) \(\mathstrut +\mathstrut 110q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 40q^{67} \) \(\mathstrut +\mathstrut 129q^{68} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut +\mathstrut 48q^{71} \) \(\mathstrut +\mathstrut 151q^{72} \) \(\mathstrut +\mathstrut 30q^{73} \) \(\mathstrut +\mathstrut 117q^{74} \) \(\mathstrut +\mathstrut 10q^{75} \) \(\mathstrut -\mathstrut 98q^{76} \) \(\mathstrut +\mathstrut 134q^{77} \) \(\mathstrut +\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 23q^{79} \) \(\mathstrut -\mathstrut 121q^{80} \) \(\mathstrut +\mathstrut 111q^{81} \) \(\mathstrut +\mathstrut 4q^{82} \) \(\mathstrut +\mathstrut 92q^{83} \) \(\mathstrut +\mathstrut 48q^{84} \) \(\mathstrut -\mathstrut 63q^{85} \) \(\mathstrut +\mathstrut 42q^{86} \) \(\mathstrut +\mathstrut 69q^{87} \) \(\mathstrut +\mathstrut 121q^{88} \) \(\mathstrut +\mathstrut 12q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut +\mathstrut 175q^{92} \) \(\mathstrut +\mathstrut 82q^{93} \) \(\mathstrut -\mathstrut 23q^{94} \) \(\mathstrut +\mathstrut 35q^{95} \) \(\mathstrut +\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 67q^{97} \) \(\mathstrut +\mathstrut 122q^{98} \) \(\mathstrut +\mathstrut 73q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.73873 0.672106 5.50064 −1.00000 −1.84072 −4.04942 −9.58729 −2.54827 2.73873
1.2 −2.68442 −1.35317 5.20611 −1.00000 3.63248 −0.554981 −8.60654 −1.16892 2.68442
1.3 −2.65256 2.52646 5.03608 −1.00000 −6.70158 −1.65453 −8.05337 3.38299 2.65256
1.4 −2.61836 3.26899 4.85584 −1.00000 −8.55940 1.91983 −7.47762 7.68627 2.61836
1.5 −2.47063 −2.44892 4.10400 −1.00000 6.05037 0.863350 −5.19820 2.99721 2.47063
1.6 −2.46463 −1.44696 4.07438 −1.00000 3.56623 3.47016 −5.11258 −0.906295 2.46463
1.7 −2.44893 0.721523 3.99726 −1.00000 −1.76696 −0.931483 −4.89116 −2.47940 2.44893
1.8 −2.44268 2.17434 3.96666 −1.00000 −5.31121 1.92177 −4.80392 1.72777 2.44268
1.9 −2.42672 −1.34880 3.88897 −1.00000 3.27316 −0.627259 −4.58399 −1.18074 2.42672
1.10 −2.38169 0.502549 3.67242 −1.00000 −1.19691 1.76739 −3.98319 −2.74744 2.38169
1.11 −2.33324 −1.40461 3.44401 −1.00000 3.27730 −3.84799 −3.36922 −1.02706 2.33324
1.12 −2.32831 1.94155 3.42102 −1.00000 −4.52053 0.423460 −3.30857 0.769626 2.32831
1.13 −2.25182 0.156734 3.07069 −1.00000 −0.352938 4.92465 −2.41100 −2.97543 2.25182
1.14 −2.23096 0.376155 2.97717 −1.00000 −0.839185 −1.46614 −2.18003 −2.85851 2.23096
1.15 −2.19837 −2.82193 2.83283 −1.00000 6.20363 2.67326 −1.83086 4.96326 2.19837
1.16 −2.17325 2.30276 2.72303 −1.00000 −5.00447 −1.58489 −1.57132 2.30268 2.17325
1.17 −2.09243 −1.43223 2.37828 −1.00000 2.99685 −1.24970 −0.791531 −0.948714 2.09243
1.18 −2.07647 −1.16893 2.31172 −1.00000 2.42725 −0.555409 −0.647270 −1.63360 2.07647
1.19 −2.04769 1.24838 2.19303 −1.00000 −2.55629 −4.80946 −0.395268 −1.44156 2.04769
1.20 −1.99934 −2.20170 1.99734 −1.00000 4.40194 0.230566 0.00531235 1.84749 1.99934
See next 80 embeddings (of 127 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.127
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(1607\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{127} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8035))\).