Properties

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

Related objects

Downloads

Learn more about

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: \(1\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 729q^{3} \) \(\mathstrut -\mathstrut 24570q^{5} \) \(\mathstrut -\mathstrut 173704q^{7} \) \(\mathstrut +\mathstrut 531441q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 729q^{3} \) \(\mathstrut -\mathstrut 24570q^{5} \) \(\mathstrut -\mathstrut 173704q^{7} \) \(\mathstrut +\mathstrut 531441q^{9} \) \(\mathstrut -\mathstrut 970164q^{11} \) \(\mathstrut -\mathstrut 24149410q^{13} \) \(\mathstrut -\mathstrut 17911530q^{15} \) \(\mathstrut -\mathstrut 157097934q^{17} \) \(\mathstrut -\mathstrut 119524780q^{19} \) \(\mathstrut -\mathstrut 126630216q^{21} \) \(\mathstrut -\mathstrut 94974984q^{23} \) \(\mathstrut -\mathstrut 617018225q^{25} \) \(\mathstrut +\mathstrut 387420489q^{27} \) \(\mathstrut +\mathstrut 4979572254q^{29} \) \(\mathstrut +\mathstrut 5638274384q^{31} \) \(\mathstrut -\mathstrut 707249556q^{33} \) \(\mathstrut +\mathstrut 4267907280q^{35} \) \(\mathstrut -\mathstrut 5881410442q^{37} \) \(\mathstrut -\mathstrut 17604919890q^{39} \) \(\mathstrut +\mathstrut 25753836330q^{41} \) \(\mathstrut -\mathstrut 68456366164q^{43} \) \(\mathstrut -\mathstrut 13057505370q^{45} \) \(\mathstrut +\mathstrut 2961760464q^{47} \) \(\mathstrut -\mathstrut 66715930791q^{49} \) \(\mathstrut -\mathstrut 114524393886q^{51} \) \(\mathstrut +\mathstrut 312742734102q^{53} \) \(\mathstrut +\mathstrut 23836929480q^{55} \) \(\mathstrut -\mathstrut 87133564620q^{57} \) \(\mathstrut +\mathstrut 461474147484q^{59} \) \(\mathstrut +\mathstrut 283119140462q^{61} \) \(\mathstrut -\mathstrut 92313427464q^{63} \) \(\mathstrut +\mathstrut 593351003700q^{65} \) \(\mathstrut -\mathstrut 1303439183836q^{67} \) \(\mathstrut -\mathstrut 69236763336q^{69} \) \(\mathstrut -\mathstrut 1263983854680q^{71} \) \(\mathstrut +\mathstrut 594014324138q^{73} \) \(\mathstrut -\mathstrut 449806286025q^{75} \) \(\mathstrut +\mathstrut 168521367456q^{77} \) \(\mathstrut -\mathstrut 1153793301952q^{79} \) \(\mathstrut +\mathstrut 282429536481q^{81} \) \(\mathstrut -\mathstrut 4820378432364q^{83} \) \(\mathstrut +\mathstrut 3859896238380q^{85} \) \(\mathstrut +\mathstrut 3630108173166q^{87} \) \(\mathstrut +\mathstrut 728548990650q^{89} \) \(\mathstrut +\mathstrut 4194849114640q^{91} \) \(\mathstrut +\mathstrut 4110302025936q^{93} \) \(\mathstrut +\mathstrut 2936723844600q^{95} \) \(\mathstrut +\mathstrut 2588736358562q^{97} \) \(\mathstrut -\mathstrut 515584926324q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −24570.0 0 −173704. 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 \(T_{5} \) \(\mathstrut +\mathstrut 24570 \) acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(12))\).