LMFDB - Space of Modular Forms of Level 12, Weight 20, and Character 12.b

Defining parameters

Level:	$ N $	=	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	=	$ 20 $
Character orbit:	$[\chi]$	=	12.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	=	$ 12 $
Character field:			$\Q$
Newforms:			$ 1 $
Sturm bound:			$40$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{20}(12, [\chi])$.

	Total	New
Modular forms	40	40
Cusp forms	36	36
Eisenstein series	4	4

Trace form

$ 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} + O(q^{10}) $

\( 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} - 4162950000q^{10} - 2268767880q^{12} - 25913431656q^{13} + 791689296672q^{16} + 2852271258192q^{18} - 1650825908424q^{21} + 7247870602416q^{22} + 23719435803936q^{24} - 118879690462380q^{25} - 7629081673968q^{28} + 37456727138640q^{30} + 529254701828640q^{33} - 248241675948480q^{34} - 1177548745309416q^{36} + 1847838600168120q^{37} - 40433256181440q^{40} - 2709671988768336q^{42} - 4365410114088000q^{45} + 17206125364795104q^{46} + 1561106052682272q^{48} - 49399737041580084q^{49} + 16558671470242896q^{52} + 40087412948587896q^{54} + 44803667812766472q^{57} - 34645536255764880q^{58} + 50260381053157440q^{60} + 174742350239997144q^{61} - 139766490424918656q^{64} - 87772097712685968q^{66} - 957190369821780672q^{69} + 244663962371376480q^{70} + 54134736422921280q^{72} - 1445122541399481432q^{73} + 2744130151937256048q^{76} + 1125465917961999024q^{78} + 1033298241353042436q^{81} + 1064985418859680800q^{82} + 1920709484261873424q^{84} - 1802899595088057600q^{85} - 9209792381828477760q^{88} - 5194944179528261040q^{90} + 6719944190337314136q^{93} - 3835186345170303552q^{94} - 11947184361208227456q^{96} + 12765226159947004488q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{20}^{\mathrm{new}}(12, [\chi])$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
12.20.b.a	$36$	$27.458$		None	$0$	$0$	$0$	$0$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	=	\( 20 \)
Character orbit:	\([\chi]\)	=	12.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 12 \)
Character field:			\(\Q\)
Newforms:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Introduction and more

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{20}^{\mathrm{new}}(12, [\chi])\) into irreducible Hecke orbits

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	12.20.b

Level	12
Weight	20
Character orbit	b
Rep. character	\(\chi_{12}(11,\cdot)\)
Character field	\(\Q\)
Dimension	36
Newforms	1
Sturm bound	40
Trace bound	0

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
12.20.b.a	\(36\)	\(27.458\)		None	\(0\)	\(0\)	\(0\)	\(0\)