Properties

Label 6014.2.a.k
Level 6014
Weight 2
Character orbit 6014.a
Self dual Yes
Analytic conductor 48.022
Analytic rank 0
Dimension 37
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: \(0\)
Dimension: \(37\)
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.

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

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 −3.24519 1.00000 −3.01148 −3.24519 −2.55038 1.00000 7.53129 −3.01148
1.2 1.00000 −3.11031 1.00000 2.99950 −3.11031 2.46329 1.00000 6.67403 2.99950
1.3 1.00000 −2.85895 1.00000 2.60012 −2.85895 −2.89016 1.00000 5.17357 2.60012
1.4 1.00000 −2.75773 1.00000 2.81004 −2.75773 5.04887 1.00000 4.60506 2.81004
1.5 1.00000 −2.56862 1.00000 −3.99872 −2.56862 2.48908 1.00000 3.59779 −3.99872
1.6 1.00000 −2.38480 1.00000 1.29081 −2.38480 −1.08194 1.00000 2.68726 1.29081
1.7 1.00000 −2.26430 1.00000 −0.734715 −2.26430 2.48512 1.00000 2.12704 −0.734715
1.8 1.00000 −2.11580 1.00000 −1.69302 −2.11580 −4.07217 1.00000 1.47662 −1.69302
1.9 1.00000 −1.95043 1.00000 −1.96504 −1.95043 0.849460 1.00000 0.804176 −1.96504
1.10 1.00000 −1.81353 1.00000 0.592127 −1.81353 0.674162 1.00000 0.288888 0.592127
1.11 1.00000 −1.30157 1.00000 3.71801 −1.30157 4.36912 1.00000 −1.30591 3.71801
1.12 1.00000 −0.850163 1.00000 1.27366 −0.850163 −2.84006 1.00000 −2.27722 1.27366
1.13 1.00000 −0.835304 1.00000 −3.09750 −0.835304 4.05347 1.00000 −2.30227 −3.09750
1.14 1.00000 −0.749812 1.00000 −0.301670 −0.749812 −4.79556 1.00000 −2.43778 −0.301670
1.15 1.00000 −0.237489 1.00000 4.10563 −0.237489 4.01630 1.00000 −2.94360 4.10563
1.16 1.00000 −0.177510 1.00000 −1.23284 −0.177510 −3.05433 1.00000 −2.96849 −1.23284
1.17 1.00000 −0.0432689 1.00000 −1.25379 −0.0432689 4.04669 1.00000 −2.99813 −1.25379
1.18 1.00000 0.242040 1.00000 −4.38700 0.242040 3.95726 1.00000 −2.94142 −4.38700
1.19 1.00000 0.277622 1.00000 −0.233184 0.277622 −0.765476 1.00000 −2.92293 −0.233184
1.20 1.00000 0.452250 1.00000 −3.58205 0.452250 −1.19090 1.00000 −2.79547 −3.58205
See all 37 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.37
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 \(T_{3}^{37} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\).