LMFDB - Newform 1.12.a.a

Newspace parameters

Level:	$ N $	=	$ 1 $
Weight:	$ k $	=	$ 12 $
Character orbit:	$[\chi]$	=	1.a (trivial)

Newform invariants

Self dual:	Yes
Analytic conductor:	$0.76834318056$
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 24q^{2} $ $\mathstrut +\mathstrut 252q^{3} $ $\mathstrut -\mathstrut 1472q^{4} $ $\mathstrut +\mathstrut 4830q^{5} $ $\mathstrut -\mathstrut 6048q^{6} $ $\mathstrut -\mathstrut 16744q^{7} $ $\mathstrut +\mathstrut 84480q^{8} $ $\mathstrut -\mathstrut 113643q^{9} $ $\mathstrut -\mathstrut 115920q^{10} $ $\mathstrut +\mathstrut 534612q^{11} $ $\mathstrut -\mathstrut 370944q^{12} $ $\mathstrut -\mathstrut 577738q^{13} $ $\mathstrut +\mathstrut 401856q^{14} $ $\mathstrut +\mathstrut 1217160q^{15} $ $\mathstrut +\mathstrut 987136q^{16} $ $\mathstrut -\mathstrut 6905934q^{17} $ $\mathstrut +\mathstrut 2727432q^{18} $ $\mathstrut +\mathstrut 10661420q^{19} $ $\mathstrut -\mathstrut 7109760q^{20} $ $\mathstrut -\mathstrut 4219488q^{21} $ $\mathstrut -\mathstrut 12830688q^{22} $ $\mathstrut +\mathstrut 18643272q^{23} $ $\mathstrut +\mathstrut 21288960q^{24} $ $\mathstrut -\mathstrut 25499225q^{25} $ $\mathstrut +\mathstrut 13865712q^{26} $ $\mathstrut -\mathstrut 73279080q^{27} $ $\mathstrut +\mathstrut 24647168q^{28} $ $\mathstrut +\mathstrut 128406630q^{29} $ $\mathstrut -\mathstrut 29211840q^{30} $ $\mathstrut -\mathstrut 52843168q^{31} $ $\mathstrut -\mathstrut 196706304q^{32} $ $\mathstrut +\mathstrut 134722224q^{33} $ $\mathstrut +\mathstrut 165742416q^{34} $ $\mathstrut -\mathstrut 80873520q^{35} $ $\mathstrut +\mathstrut 167282496q^{36} $ $\mathstrut -\mathstrut 182213314q^{37} $ $\mathstrut -\mathstrut 255874080q^{38} $ $\mathstrut -\mathstrut 145589976q^{39} $ $\mathstrut +\mathstrut 408038400q^{40} $ $\mathstrut +\mathstrut 308120442q^{41} $ $\mathstrut +\mathstrut 101267712q^{42} $ $\mathstrut -\mathstrut 17125708q^{43} $ $\mathstrut -\mathstrut 786948864q^{44} $ $\mathstrut -\mathstrut 548895690q^{45} $ $\mathstrut -\mathstrut 447438528q^{46} $ $\mathstrut +\mathstrut 2687348496q^{47} $ $\mathstrut +\mathstrut 248758272q^{48} $ $\mathstrut -\mathstrut 1696965207q^{49} $ $\mathstrut +\mathstrut 611981400q^{50} $ $\mathstrut -\mathstrut 1740295368q^{51} $ $\mathstrut +\mathstrut 850430336q^{52} $ $\mathstrut -\mathstrut 1596055698q^{53} $ $\mathstrut +\mathstrut 1758697920q^{54} $ $\mathstrut +\mathstrut 2582175960q^{55} $ $\mathstrut -\mathstrut 1414533120q^{56} $ $\mathstrut +\mathstrut 2686677840q^{57} $ $\mathstrut -\mathstrut 3081759120q^{58} $ $\mathstrut -\mathstrut 5189203740q^{59} $ $\mathstrut -\mathstrut 1791659520q^{60} $ $\mathstrut +\mathstrut 6956478662q^{61} $ $\mathstrut +\mathstrut 1268236032q^{62} $ $\mathstrut +\mathstrut 1902838392q^{63} $ $\mathstrut +\mathstrut 2699296768q^{64} $ $\mathstrut -\mathstrut 2790474540q^{65} $ $\mathstrut -\mathstrut 3233333376q^{66} $ $\mathstrut -\mathstrut 15481826884q^{67} $ $\mathstrut +\mathstrut 10165534848q^{68} $ $\mathstrut +\mathstrut 4698104544q^{69} $ $\mathstrut +\mathstrut 1940964480q^{70} $ $\mathstrut +\mathstrut 9791485272q^{71} $ $\mathstrut -\mathstrut 9600560640q^{72} $ $\mathstrut +\mathstrut 1463791322q^{73} $ $\mathstrut +\mathstrut 4373119536q^{74} $ $\mathstrut -\mathstrut 6425804700q^{75} $ $\mathstrut -\mathstrut 15693610240q^{76} $ $\mathstrut -\mathstrut 8951543328q^{77} $ $\mathstrut +\mathstrut 3494159424q^{78} $ $\mathstrut +\mathstrut 38116845680q^{79} $ $\mathstrut +\mathstrut 4767866880q^{80} $ $\mathstrut +\mathstrut 1665188361q^{81} $ $\mathstrut -\mathstrut 7394890608q^{82} $ $\mathstrut -\mathstrut 29335099668q^{83} $ $\mathstrut +\mathstrut 6211086336q^{84} $ $\mathstrut -\mathstrut 33355661220q^{85} $ $\mathstrut +\mathstrut 411016992q^{86} $ $\mathstrut +\mathstrut 32358470760q^{87} $ $\mathstrut +\mathstrut 45164021760q^{88} $ $\mathstrut -\mathstrut 24992917110q^{89} $ $\mathstrut +\mathstrut 13173496560q^{90} $ $\mathstrut +\mathstrut 9673645072q^{91} $ $\mathstrut -\mathstrut 27442896384q^{92} $ $\mathstrut -\mathstrut 13316478336q^{93} $ $\mathstrut -\mathstrut 64496363904q^{94} $ $\mathstrut +\mathstrut 51494658600q^{95} $ $\mathstrut -\mathstrut 49569988608q^{96} $ $\mathstrut +\mathstrut 75013568546q^{97} $ $\mathstrut +\mathstrut 40727164968q^{98} $ $\mathstrut -\mathstrut 60754911516q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

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

−24.0000

252.000

−1472.00

4830.00

−6048.00

−16744.0

84480.0

−113643.

−115920.

Inner twists

This newform does not admit any (nontrivial) inner twists.

Hecke kernels

There are no other newforms in $S_{12}^{\mathrm{new}}(\Gamma_0(1))$.

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 1 \)
Weight:	\( k \)	=	\( 12 \)
Character orbit:	\([\chi]\)	=	1.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
Format:

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