Properties

Label 6014.2.a.f
Level 6014
Weight 2
Character orbit 6014.a
Self dual Yes
Analytic conductor 48.022
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0220317756\)
Analytic rank: \(1\)
Dimension: \(22\)
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.

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

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 −1.00000 −2.92127 1.00000 −1.99624 2.92127 −0.468229 −1.00000 5.53384 1.99624
1.2 −1.00000 −2.80047 1.00000 0.364133 2.80047 1.53058 −1.00000 4.84261 −0.364133
1.3 −1.00000 −2.51447 1.00000 3.35437 2.51447 0.494792 −1.00000 3.32256 −3.35437
1.4 −1.00000 −2.06526 1.00000 1.84106 2.06526 0.807248 −1.00000 1.26528 −1.84106
1.5 −1.00000 −1.79599 1.00000 −3.70171 1.79599 −3.49561 −1.00000 0.225587 3.70171
1.6 −1.00000 −1.60979 1.00000 1.84866 1.60979 −2.27059 −1.00000 −0.408562 −1.84866
1.7 −1.00000 −1.34015 1.00000 0.146848 1.34015 4.48511 −1.00000 −1.20399 −0.146848
1.8 −1.00000 −1.04488 1.00000 −0.722746 1.04488 −0.912399 −1.00000 −1.90823 0.722746
1.9 −1.00000 −0.916242 1.00000 −2.81390 0.916242 0.508180 −1.00000 −2.16050 2.81390
1.10 −1.00000 −0.531212 1.00000 1.86385 0.531212 −4.06404 −1.00000 −2.71781 −1.86385
1.11 −1.00000 0.0685928 1.00000 −2.24786 −0.0685928 −4.29331 −1.00000 −2.99530 2.24786
1.12 −1.00000 0.191955 1.00000 −1.50666 −0.191955 −2.08203 −1.00000 −2.96315 1.50666
1.13 −1.00000 0.253397 1.00000 −0.480250 −0.253397 2.09789 −1.00000 −2.93579 0.480250
1.14 −1.00000 0.813553 1.00000 3.21035 −0.813553 −2.44817 −1.00000 −2.33813 −3.21035
1.15 −1.00000 1.04707 1.00000 1.01417 −1.04707 3.78577 −1.00000 −1.90364 −1.01417
1.16 −1.00000 1.29017 1.00000 3.44095 −1.29017 −0.471801 −1.00000 −1.33547 −3.44095
1.17 −1.00000 1.47323 1.00000 −3.13161 −1.47323 0.874706 −1.00000 −0.829602 3.13161
1.18 −1.00000 2.07834 1.00000 −0.312935 −2.07834 0.578926 −1.00000 1.31950 0.312935
1.19 −1.00000 2.17019 1.00000 1.18841 −2.17019 −1.11869 −1.00000 1.70972 −1.18841
1.20 −1.00000 2.25454 1.00000 −2.47204 −2.25454 0.953481 −1.00000 2.08293 2.47204
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(31\) \(-1\)
\(97\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{22} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\).