Properties

Label 14.4.a.a
Level 14
Weight 4
Character orbit 14.a
Self dual Yes
Analytic conductor 0.826
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 14.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.82602674008\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 37q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 37q^{9} \) \(\mathstrut +\mathstrut 28q^{10} \) \(\mathstrut -\mathstrut 28q^{11} \) \(\mathstrut +\mathstrut 32q^{12} \) \(\mathstrut +\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 112q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 74q^{17} \) \(\mathstrut -\mathstrut 74q^{18} \) \(\mathstrut +\mathstrut 80q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut -\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 56q^{22} \) \(\mathstrut -\mathstrut 112q^{23} \) \(\mathstrut -\mathstrut 64q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 80q^{27} \) \(\mathstrut -\mathstrut 28q^{28} \) \(\mathstrut +\mathstrut 190q^{29} \) \(\mathstrut +\mathstrut 224q^{30} \) \(\mathstrut +\mathstrut 72q^{31} \) \(\mathstrut -\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 224q^{33} \) \(\mathstrut -\mathstrut 148q^{34} \) \(\mathstrut +\mathstrut 98q^{35} \) \(\mathstrut +\mathstrut 148q^{36} \) \(\mathstrut -\mathstrut 346q^{37} \) \(\mathstrut -\mathstrut 160q^{38} \) \(\mathstrut +\mathstrut 144q^{39} \) \(\mathstrut +\mathstrut 112q^{40} \) \(\mathstrut +\mathstrut 162q^{41} \) \(\mathstrut +\mathstrut 112q^{42} \) \(\mathstrut -\mathstrut 412q^{43} \) \(\mathstrut -\mathstrut 112q^{44} \) \(\mathstrut -\mathstrut 518q^{45} \) \(\mathstrut +\mathstrut 224q^{46} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 49q^{49} \) \(\mathstrut -\mathstrut 142q^{50} \) \(\mathstrut +\mathstrut 592q^{51} \) \(\mathstrut +\mathstrut 72q^{52} \) \(\mathstrut +\mathstrut 318q^{53} \) \(\mathstrut -\mathstrut 160q^{54} \) \(\mathstrut +\mathstrut 392q^{55} \) \(\mathstrut +\mathstrut 56q^{56} \) \(\mathstrut +\mathstrut 640q^{57} \) \(\mathstrut -\mathstrut 380q^{58} \) \(\mathstrut -\mathstrut 200q^{59} \) \(\mathstrut -\mathstrut 448q^{60} \) \(\mathstrut -\mathstrut 198q^{61} \) \(\mathstrut -\mathstrut 144q^{62} \) \(\mathstrut -\mathstrut 259q^{63} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut -\mathstrut 252q^{65} \) \(\mathstrut +\mathstrut 448q^{66} \) \(\mathstrut -\mathstrut 716q^{67} \) \(\mathstrut +\mathstrut 296q^{68} \) \(\mathstrut -\mathstrut 896q^{69} \) \(\mathstrut -\mathstrut 196q^{70} \) \(\mathstrut +\mathstrut 392q^{71} \) \(\mathstrut -\mathstrut 296q^{72} \) \(\mathstrut +\mathstrut 538q^{73} \) \(\mathstrut +\mathstrut 692q^{74} \) \(\mathstrut +\mathstrut 568q^{75} \) \(\mathstrut +\mathstrut 320q^{76} \) \(\mathstrut +\mathstrut 196q^{77} \) \(\mathstrut -\mathstrut 288q^{78} \) \(\mathstrut +\mathstrut 240q^{79} \) \(\mathstrut -\mathstrut 224q^{80} \) \(\mathstrut -\mathstrut 359q^{81} \) \(\mathstrut -\mathstrut 324q^{82} \) \(\mathstrut -\mathstrut 1072q^{83} \) \(\mathstrut -\mathstrut 224q^{84} \) \(\mathstrut -\mathstrut 1036q^{85} \) \(\mathstrut +\mathstrut 824q^{86} \) \(\mathstrut +\mathstrut 1520q^{87} \) \(\mathstrut +\mathstrut 224q^{88} \) \(\mathstrut +\mathstrut 810q^{89} \) \(\mathstrut +\mathstrut 1036q^{90} \) \(\mathstrut -\mathstrut 126q^{91} \) \(\mathstrut -\mathstrut 448q^{92} \) \(\mathstrut +\mathstrut 576q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 1120q^{95} \) \(\mathstrut -\mathstrut 256q^{96} \) \(\mathstrut +\mathstrut 1354q^{97} \) \(\mathstrut -\mathstrut 98q^{98} \) \(\mathstrut -\mathstrut 1036q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
−2.00000 8.00000 4.00000 −14.0000 −16.0000 −7.00000 −8.00000 37.0000 28.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3} \) \(\mathstrut -\mathstrut 8 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(14))\).