Properties

Label 12.14.a.a
Level 12
Weight 14
Character orbit 12.a
Self dual Yes
Analytic conductor 12.868
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 12.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(12.8677114742\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 729q^{3} \) \(\mathstrut -\mathstrut 14850q^{5} \) \(\mathstrut -\mathstrut 62896q^{7} \) \(\mathstrut +\mathstrut 531441q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 729q^{3} \) \(\mathstrut -\mathstrut 14850q^{5} \) \(\mathstrut -\mathstrut 62896q^{7} \) \(\mathstrut +\mathstrut 531441q^{9} \) \(\mathstrut +\mathstrut 5104836q^{11} \) \(\mathstrut +\mathstrut 11484110q^{13} \) \(\mathstrut +\mathstrut 10825650q^{15} \) \(\mathstrut +\mathstrut 119964834q^{17} \) \(\mathstrut +\mathstrut 332601020q^{19} \) \(\mathstrut +\mathstrut 45851184q^{21} \) \(\mathstrut +\mathstrut 350924184q^{23} \) \(\mathstrut -\mathstrut 1000180625q^{25} \) \(\mathstrut -\mathstrut 387420489q^{27} \) \(\mathstrut -\mathstrut 1761101946q^{29} \) \(\mathstrut -\mathstrut 3934224616q^{31} \) \(\mathstrut -\mathstrut 3721425444q^{33} \) \(\mathstrut +\mathstrut 934005600q^{35} \) \(\mathstrut -\mathstrut 7803567658q^{37} \) \(\mathstrut -\mathstrut 8371916190q^{39} \) \(\mathstrut +\mathstrut 52882647930q^{41} \) \(\mathstrut +\mathstrut 26018412164q^{43} \) \(\mathstrut -\mathstrut 7891898850q^{45} \) \(\mathstrut +\mathstrut 142370739936q^{47} \) \(\mathstrut -\mathstrut 92933103591q^{49} \) \(\mathstrut -\mathstrut 87454363986q^{51} \) \(\mathstrut +\mathstrut 13770034398q^{53} \) \(\mathstrut -\mathstrut 75806814600q^{55} \) \(\mathstrut -\mathstrut 242466143580q^{57} \) \(\mathstrut +\mathstrut 336464984484q^{59} \) \(\mathstrut -\mathstrut 677260793938q^{61} \) \(\mathstrut -\mathstrut 33425513136q^{63} \) \(\mathstrut -\mathstrut 170539033500q^{65} \) \(\mathstrut +\mathstrut 262301598236q^{67} \) \(\mathstrut -\mathstrut 255823730136q^{69} \) \(\mathstrut +\mathstrut 1594961300520q^{71} \) \(\mathstrut +\mathstrut 578812819562q^{73} \) \(\mathstrut +\mathstrut 729131675625q^{75} \) \(\mathstrut -\mathstrut 321073765056q^{77} \) \(\mathstrut +\mathstrut 2495818789448q^{79} \) \(\mathstrut +\mathstrut 282429536481q^{81} \) \(\mathstrut -\mathstrut 2693235578436q^{83} \) \(\mathstrut -\mathstrut 1781477784900q^{85} \) \(\mathstrut +\mathstrut 1283843318634q^{87} \) \(\mathstrut -\mathstrut 7935538832550q^{89} \) \(\mathstrut -\mathstrut 722304582560q^{91} \) \(\mathstrut +\mathstrut 2868049745064q^{93} \) \(\mathstrut -\mathstrut 4939125147000q^{95} \) \(\mathstrut -\mathstrut 7858601662q^{97} \) \(\mathstrut +\mathstrut 2712919148676q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
0 −729.000 0 −14850.0 0 −62896.0 0 531441. 0
\(n\): 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
\(2\) \(-1\)
\(3\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{5} \) \(\mathstrut +\mathstrut 14850 \) acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(12))\).