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

Related objects

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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

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

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 \( T_{3} - 8 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(14))\).