LMFDB - Space of Modular Forms of Level 1 and Weight 12

Defining parameters

Level:	$ N $	=	$ 1 $
Weight:	$ k $	=	$ 12 $
Nonzero newspaces:			$ 1 $
Newform subspaces:			$ 1 $
Sturm bound:			$1$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{12}(\Gamma_1(1))$.

	Total	New
Modular forms	2	2
Cusp forms	1	1
Eisenstein series	1	1

Trace form

$ q - 24q^{2} + 252q^{3} - 1472q^{4} + 4830q^{5} - 6048q^{6} - 16744q^{7} + 84480q^{8} - 113643q^{9} + O(q^{10}) $

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

Display 100 coefficients 10 coefficients

Decomposition of $S_{12}^{\mathrm{new}}(\Gamma_1(1))$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $ S_k^{\mathrm{new}}(N, \chi) $ we list the newforms together with their dimension.

Label	$\chi$	Newforms	Dimension	$\chi$ degree
1.12.a	$\chi_{1}(1, \cdot)$	1.12.a.a	1	1

Hecke Characteristic Polynomials

$p$	$F_p(T)$
$2$	$ 1 + 24 T + 2048 T^{2} $
$3$	$ 1 - 252 T + 177147 T^{2} $
$5$	$ 1 - 4830 T + 48828125 T^{2} $
$7$	$ 1 + 16744 T + 1977326743 T^{2} $
$11$	$ 1 - 534612 T + 285311670611 T^{2} $
$13$	$ 1 + 577738 T + 1792160394037 T^{2} $
$17$	$ 1 + 6905934 T + 34271896307633 T^{2} $
$19$	$ 1 - 10661420 T + 116490258898219 T^{2} $
$23$	$ 1 - 18643272 T + 952809757913927 T^{2} $
$29$	$ 1 - 128406630 T + 12200509765705829 T^{2} $
$31$	$ 1 + 52843168 T + 25408476896404831 T^{2} $
$37$	$ 1 + 182213314 T + 177917621779460413 T^{2} $
$41$	$ 1 - 308120442 T + 550329031716248441 T^{2} $
$43$	$ 1 + 17125708 T + 929293739471222707 T^{2} $
$47$	$ 1 - 2687348496 T + 2472159215084012303 T^{2} $
$53$	$ 1 + 1596055698 T + 9269035929372191597 T^{2} $
$59$	$ 1 + 5189203740 T + 30155888444737842659 T^{2} $
$61$	$ 1 - 6956478662 T + 43513917611435838661 T^{2} $
$67$	$ 1 + 15481826884 T + $$12\!\cdots\!83$$ T^{2} $
$71$	$ 1 - 9791485272 T + $$23\!\cdots\!71$$ T^{2} $
$73$	$ 1 - 1463791322 T + $$31\!\cdots\!77$$ T^{2} $
$79$	$ 1 - 38116845680 T + $$74\!\cdots\!79$$ T^{2} $
$83$	$ 1 + 29335099668 T + $$12\!\cdots\!67$$ T^{2} $
$89$	$ 1 + 24992917110 T + $$27\!\cdots\!89$$ T^{2} $
$97$	$ 1 - 75013568546 T + $$71\!\cdots\!53$$ T^{2} $
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Introduction	Features
Universe	News

Level:	\( N \)	=	\( 1 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1\)
Trace bound:			\(0\)

Introduction and more

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)

Hecke Characteristic Polynomials

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1.12

Level	1
Weight	12
Dimension	1
Nonzero newspaces	1
Newform subspaces	1
Sturm bound	1
Trace bound	0

$p$	$F_p(T)$
$2$	\( 1 + 24 T + 2048 T^{2} \)
$3$	\( 1 - 252 T + 177147 T^{2} \)
$5$	\( 1 - 4830 T + 48828125 T^{2} \)
$7$	\( 1 + 16744 T + 1977326743 T^{2} \)
$11$	\( 1 - 534612 T + 285311670611 T^{2} \)
$13$	\( 1 + 577738 T + 1792160394037 T^{2} \)
$17$	\( 1 + 6905934 T + 34271896307633 T^{2} \)
$19$	\( 1 - 10661420 T + 116490258898219 T^{2} \)
$23$	\( 1 - 18643272 T + 952809757913927 T^{2} \)
$29$	\( 1 - 128406630 T + 12200509765705829 T^{2} \)
$31$	\( 1 + 52843168 T + 25408476896404831 T^{2} \)
$37$	\( 1 + 182213314 T + 177917621779460413 T^{2} \)
$41$	\( 1 - 308120442 T + 550329031716248441 T^{2} \)
$43$	\( 1 + 17125708 T + 929293739471222707 T^{2} \)
$47$	\( 1 - 2687348496 T + 2472159215084012303 T^{2} \)
$53$	\( 1 + 1596055698 T + 9269035929372191597 T^{2} \)
$59$	\( 1 + 5189203740 T + 30155888444737842659 T^{2} \)
$61$	\( 1 - 6956478662 T + 43513917611435838661 T^{2} \)
$67$	\( 1 + 15481826884 T + \)\(12\!\cdots\!83\)\( T^{2} \)
$71$	\( 1 - 9791485272 T + \)\(23\!\cdots\!71\)\( T^{2} \)
$73$	\( 1 - 1463791322 T + \)\(31\!\cdots\!77\)\( T^{2} \)
$79$	\( 1 - 38116845680 T + \)\(74\!\cdots\!79\)\( T^{2} \)
$83$	\( 1 + 29335099668 T + \)\(12\!\cdots\!67\)\( T^{2} \)
$89$	\( 1 + 24992917110 T + \)\(27\!\cdots\!89\)\( T^{2} \)
$97$	\( 1 - 75013568546 T + \)\(71\!\cdots\!53\)\( T^{2} \)
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