Properties

Label 6014.2.a.l
Level 6014
Weight 2
Character orbit 6014.a
Self dual Yes
Analytic conductor 48.022
Analytic rank 0
Dimension 38
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: \(38\)
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.

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

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 −3.36850 1.00000 3.93449 3.36850 −2.34410 −1.00000 8.34681 −3.93449
1.2 −1.00000 −3.27880 1.00000 0.401675 3.27880 −4.68111 −1.00000 7.75051 −0.401675
1.3 −1.00000 −3.21269 1.00000 −0.168256 3.21269 2.46391 −1.00000 7.32140 0.168256
1.4 −1.00000 −3.06494 1.00000 −3.85153 3.06494 4.92968 −1.00000 6.39384 3.85153
1.5 −1.00000 −2.46616 1.00000 −2.24161 2.46616 4.72952 −1.00000 3.08193 2.24161
1.6 −1.00000 −2.41930 1.00000 0.0104516 2.41930 −3.11450 −1.00000 2.85300 −0.0104516
1.7 −1.00000 −2.33846 1.00000 2.68670 2.33846 5.16448 −1.00000 2.46841 −2.68670
1.8 −1.00000 −2.25991 1.00000 3.07445 2.25991 −1.73147 −1.00000 2.10720 −3.07445
1.9 −1.00000 −2.22677 1.00000 −4.13450 2.22677 −4.78775 −1.00000 1.95850 4.13450
1.10 −1.00000 −2.20978 1.00000 −2.38189 2.20978 −2.04649 −1.00000 1.88314 2.38189
1.11 −1.00000 −1.71746 1.00000 −1.04814 1.71746 0.0655046 −1.00000 −0.0503220 1.04814
1.12 −1.00000 −1.56405 1.00000 2.83927 1.56405 2.44268 −1.00000 −0.553753 −2.83927
1.13 −1.00000 −1.31913 1.00000 1.08741 1.31913 −0.837035 −1.00000 −1.25989 −1.08741
1.14 −1.00000 −1.26759 1.00000 −3.06753 1.26759 1.65725 −1.00000 −1.39322 3.06753
1.15 −1.00000 −1.26563 1.00000 1.94989 1.26563 −2.66768 −1.00000 −1.39817 −1.94989
1.16 −1.00000 −0.885413 1.00000 −0.534430 0.885413 1.09138 −1.00000 −2.21604 0.534430
1.17 −1.00000 −0.717443 1.00000 3.51838 0.717443 −3.26736 −1.00000 −2.48528 −3.51838
1.18 −1.00000 −0.679880 1.00000 −4.32143 0.679880 1.08152 −1.00000 −2.53776 4.32143
1.19 −1.00000 −0.181456 1.00000 3.41962 0.181456 3.19929 −1.00000 −2.96707 −3.41962
1.20 −1.00000 −0.173832 1.00000 −1.31890 0.173832 −4.23696 −1.00000 −2.96978 1.31890
See all 38 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.38
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 \(T_{3}^{38} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\).