Properties

Label 12.10.a.a
Level 12
Weight 10
Character orbit 12.a
Self dual Yes
Analytic conductor 6.180
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 12.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(6.18043003397\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 81q^{3} \) \(\mathstrut +\mathstrut 990q^{5} \) \(\mathstrut +\mathstrut 8576q^{7} \) \(\mathstrut +\mathstrut 6561q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 81q^{3} \) \(\mathstrut +\mathstrut 990q^{5} \) \(\mathstrut +\mathstrut 8576q^{7} \) \(\mathstrut +\mathstrut 6561q^{9} \) \(\mathstrut +\mathstrut 70596q^{11} \) \(\mathstrut -\mathstrut 2530q^{13} \) \(\mathstrut -\mathstrut 80190q^{15} \) \(\mathstrut -\mathstrut 200574q^{17} \) \(\mathstrut -\mathstrut 695620q^{19} \) \(\mathstrut -\mathstrut 694656q^{21} \) \(\mathstrut +\mathstrut 2472696q^{23} \) \(\mathstrut -\mathstrut 973025q^{25} \) \(\mathstrut -\mathstrut 531441q^{27} \) \(\mathstrut +\mathstrut 5474214q^{29} \) \(\mathstrut +\mathstrut 3732104q^{31} \) \(\mathstrut -\mathstrut 5718276q^{33} \) \(\mathstrut +\mathstrut 8490240q^{35} \) \(\mathstrut -\mathstrut 21898522q^{37} \) \(\mathstrut +\mathstrut 204930q^{39} \) \(\mathstrut -\mathstrut 23818950q^{41} \) \(\mathstrut +\mathstrut 10612676q^{43} \) \(\mathstrut +\mathstrut 6495390q^{45} \) \(\mathstrut +\mathstrut 2398464q^{47} \) \(\mathstrut +\mathstrut 33194169q^{49} \) \(\mathstrut +\mathstrut 16246494q^{51} \) \(\mathstrut -\mathstrut 8994978q^{53} \) \(\mathstrut +\mathstrut 69890040q^{55} \) \(\mathstrut +\mathstrut 56345220q^{57} \) \(\mathstrut -\mathstrut 143417916q^{59} \) \(\mathstrut -\mathstrut 19804258q^{61} \) \(\mathstrut +\mathstrut 56267136q^{63} \) \(\mathstrut -\mathstrut 2504700q^{65} \) \(\mathstrut -\mathstrut 165625156q^{67} \) \(\mathstrut -\mathstrut 200288376q^{69} \) \(\mathstrut -\mathstrut 194801400q^{71} \) \(\mathstrut +\mathstrut 148729418q^{73} \) \(\mathstrut +\mathstrut 78815025q^{75} \) \(\mathstrut +\mathstrut 605431296q^{77} \) \(\mathstrut -\mathstrut 30134152q^{79} \) \(\mathstrut +\mathstrut 43046721q^{81} \) \(\mathstrut +\mathstrut 302054076q^{83} \) \(\mathstrut -\mathstrut 198568260q^{85} \) \(\mathstrut -\mathstrut 443411334q^{87} \) \(\mathstrut +\mathstrut 909502650q^{89} \) \(\mathstrut -\mathstrut 21697280q^{91} \) \(\mathstrut -\mathstrut 302300424q^{93} \) \(\mathstrut -\mathstrut 688663800q^{95} \) \(\mathstrut -\mathstrut 872463358q^{97} \) \(\mathstrut +\mathstrut 463180356q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −81.0000 0 990.000 0 8576.00 0 6561.00 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

There are no other newforms in \(S_{10}^{\mathrm{new}}(\Gamma_0(12))\).