Properties

Label 14.12.a.b
Level 14
Weight 12
Character orbit 14.a
Self dual Yes
Analytic conductor 10.757
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 14.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(10.7568045278\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut -\mathstrut 90q^{3} \) \(\mathstrut +\mathstrut 1024q^{4} \) \(\mathstrut -\mathstrut 7480q^{5} \) \(\mathstrut -\mathstrut 2880q^{6} \) \(\mathstrut -\mathstrut 16807q^{7} \) \(\mathstrut +\mathstrut 32768q^{8} \) \(\mathstrut -\mathstrut 169047q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut -\mathstrut 90q^{3} \) \(\mathstrut +\mathstrut 1024q^{4} \) \(\mathstrut -\mathstrut 7480q^{5} \) \(\mathstrut -\mathstrut 2880q^{6} \) \(\mathstrut -\mathstrut 16807q^{7} \) \(\mathstrut +\mathstrut 32768q^{8} \) \(\mathstrut -\mathstrut 169047q^{9} \) \(\mathstrut -\mathstrut 239360q^{10} \) \(\mathstrut -\mathstrut 294536q^{11} \) \(\mathstrut -\mathstrut 92160q^{12} \) \(\mathstrut -\mathstrut 210588q^{13} \) \(\mathstrut -\mathstrut 537824q^{14} \) \(\mathstrut +\mathstrut 673200q^{15} \) \(\mathstrut +\mathstrut 1048576q^{16} \) \(\mathstrut -\mathstrut 6962906q^{17} \) \(\mathstrut -\mathstrut 5409504q^{18} \) \(\mathstrut -\mathstrut 9346390q^{19} \) \(\mathstrut -\mathstrut 7659520q^{20} \) \(\mathstrut +\mathstrut 1512630q^{21} \) \(\mathstrut -\mathstrut 9425152q^{22} \) \(\mathstrut +\mathstrut 51172000q^{23} \) \(\mathstrut -\mathstrut 2949120q^{24} \) \(\mathstrut +\mathstrut 7122275q^{25} \) \(\mathstrut -\mathstrut 6738816q^{26} \) \(\mathstrut +\mathstrut 31157460q^{27} \) \(\mathstrut -\mathstrut 17210368q^{28} \) \(\mathstrut +\mathstrut 166196354q^{29} \) \(\mathstrut +\mathstrut 21542400q^{30} \) \(\mathstrut +\mathstrut 119000988q^{31} \) \(\mathstrut +\mathstrut 33554432q^{32} \) \(\mathstrut +\mathstrut 26508240q^{33} \) \(\mathstrut -\mathstrut 222812992q^{34} \) \(\mathstrut +\mathstrut 125716360q^{35} \) \(\mathstrut -\mathstrut 173104128q^{36} \) \(\mathstrut -\mathstrut 275545510q^{37} \) \(\mathstrut -\mathstrut 299084480q^{38} \) \(\mathstrut +\mathstrut 18952920q^{39} \) \(\mathstrut -\mathstrut 245104640q^{40} \) \(\mathstrut -\mathstrut 197988378q^{41} \) \(\mathstrut +\mathstrut 48404160q^{42} \) \(\mathstrut -\mathstrut 809489728q^{43} \) \(\mathstrut -\mathstrut 301604864q^{44} \) \(\mathstrut +\mathstrut 1264471560q^{45} \) \(\mathstrut +\mathstrut 1637504000q^{46} \) \(\mathstrut -\mathstrut 2600196204q^{47} \) \(\mathstrut -\mathstrut 94371840q^{48} \) \(\mathstrut +\mathstrut 282475249q^{49} \) \(\mathstrut +\mathstrut 227912800q^{50} \) \(\mathstrut +\mathstrut 626661540q^{51} \) \(\mathstrut -\mathstrut 215642112q^{52} \) \(\mathstrut +\mathstrut 733631454q^{53} \) \(\mathstrut +\mathstrut 997038720q^{54} \) \(\mathstrut +\mathstrut 2203129280q^{55} \) \(\mathstrut -\mathstrut 550731776q^{56} \) \(\mathstrut +\mathstrut 841175100q^{57} \) \(\mathstrut +\mathstrut 5318283328q^{58} \) \(\mathstrut -\mathstrut 4657126942q^{59} \) \(\mathstrut +\mathstrut 689356800q^{60} \) \(\mathstrut -\mathstrut 5135837424q^{61} \) \(\mathstrut +\mathstrut 3808031616q^{62} \) \(\mathstrut +\mathstrut 2841172929q^{63} \) \(\mathstrut +\mathstrut 1073741824q^{64} \) \(\mathstrut +\mathstrut 1575198240q^{65} \) \(\mathstrut +\mathstrut 848263680q^{66} \) \(\mathstrut +\mathstrut 8810564836q^{67} \) \(\mathstrut -\mathstrut 7130015744q^{68} \) \(\mathstrut -\mathstrut 4605480000q^{69} \) \(\mathstrut +\mathstrut 4022923520q^{70} \) \(\mathstrut -\mathstrut 3849006656q^{71} \) \(\mathstrut -\mathstrut 5539332096q^{72} \) \(\mathstrut -\mathstrut 18686748254q^{73} \) \(\mathstrut -\mathstrut 8817456320q^{74} \) \(\mathstrut -\mathstrut 641004750q^{75} \) \(\mathstrut -\mathstrut 9570703360q^{76} \) \(\mathstrut +\mathstrut 4950266552q^{77} \) \(\mathstrut +\mathstrut 606493440q^{78} \) \(\mathstrut -\mathstrut 29850061992q^{79} \) \(\mathstrut -\mathstrut 7843348480q^{80} \) \(\mathstrut +\mathstrut 27141997509q^{81} \) \(\mathstrut -\mathstrut 6335628096q^{82} \) \(\mathstrut -\mathstrut 5875980446q^{83} \) \(\mathstrut +\mathstrut 1548933120q^{84} \) \(\mathstrut +\mathstrut 52082536880q^{85} \) \(\mathstrut -\mathstrut 25903671296q^{86} \) \(\mathstrut -\mathstrut 14957671860q^{87} \) \(\mathstrut -\mathstrut 9651355648q^{88} \) \(\mathstrut +\mathstrut 83056539450q^{89} \) \(\mathstrut +\mathstrut 40463089920q^{90} \) \(\mathstrut +\mathstrut 3539352516q^{91} \) \(\mathstrut +\mathstrut 52400128000q^{92} \) \(\mathstrut -\mathstrut 10710088920q^{93} \) \(\mathstrut -\mathstrut 83206278528q^{94} \) \(\mathstrut +\mathstrut 69910997200q^{95} \) \(\mathstrut -\mathstrut 3019898880q^{96} \) \(\mathstrut +\mathstrut 149400800374q^{97} \) \(\mathstrut +\mathstrut 9039207968q^{98} \) \(\mathstrut +\mathstrut 49790427192q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
32.0000 −90.0000 1024.00 −7480.00 −2880.00 −16807.0 32768.0 −169047. −239360.
\(n\): 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 \(T_{3} \) \(\mathstrut +\mathstrut 90 \) acting on \(S_{12}^{\mathrm{new}}(\Gamma_0(14))\).