LMFDB - Space of Modular Forms of Level 143, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 143 = 11 \cdot 13 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	143.a (trivial)
Character field:			$\Q$
Newforms:			$ 3 $
Sturm bound:			$28$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(143))$.

	Total	New	Old
Modular forms	16	11	5
Cusp forms	13	11	2
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$11$	$13$	Fricke	Dim.
$+$	$+$	$+$	$1$
$+$	$-$	$-$	$6$
$-$	$+$	$-$	$4$
Plus space		$+$	$1$
Minus space		$-$	$10$

Trace form

$11q $ $\mathstrut +\mathstrut 3q^{2} $ $\mathstrut +\mathstrut 2q^{3} $ $\mathstrut +\mathstrut 9q^{4} $ $\mathstrut -\mathstrut 4q^{6} $ $\mathstrut +\mathstrut 8q^{7} $ $\mathstrut +\mathstrut 3q^{8} $ $\mathstrut +\mathstrut 13q^{9} $ $\mathstrut -\mathstrut 2q^{10} $ $\mathstrut -\mathstrut 3q^{11} $ $\mathstrut +\mathstrut q^{13} $ $\mathstrut -\mathstrut 16q^{14} $ $\mathstrut -\mathstrut 6q^{15} $ $\mathstrut +\mathstrut 17q^{16} $ $\mathstrut +\mathstrut 2q^{17} $ $\mathstrut -\mathstrut 9q^{18} $ $\mathstrut -\mathstrut 18q^{20} $ $\mathstrut -\mathstrut 12q^{21} $ $\mathstrut +\mathstrut 3q^{22} $ $\mathstrut +\mathstrut 14q^{23} $ $\mathstrut -\mathstrut 36q^{24} $ $\mathstrut +\mathstrut 31q^{25} $ $\mathstrut -\mathstrut 3q^{26} $ $\mathstrut +\mathstrut 2q^{27} $ $\mathstrut +\mathstrut 12q^{28} $ $\mathstrut -\mathstrut 10q^{29} $ $\mathstrut -\mathstrut 48q^{30} $ $\mathstrut -\mathstrut 10q^{31} $ $\mathstrut -\mathstrut 21q^{32} $ $\mathstrut -\mathstrut 2q^{33} $ $\mathstrut -\mathstrut 34q^{34} $ $\mathstrut -\mathstrut 28q^{35} $ $\mathstrut -\mathstrut 13q^{36} $ $\mathstrut +\mathstrut 16q^{37} $ $\mathstrut -\mathstrut 14q^{38} $ $\mathstrut +\mathstrut 4q^{39} $ $\mathstrut -\mathstrut 14q^{40} $ $\mathstrut +\mathstrut 14q^{41} $ $\mathstrut +\mathstrut 6q^{42} $ $\mathstrut +\mathstrut 20q^{43} $ $\mathstrut -\mathstrut 3q^{44} $ $\mathstrut +\mathstrut 2q^{45} $ $\mathstrut -\mathstrut 16q^{47} $ $\mathstrut -\mathstrut 6q^{48} $ $\mathstrut +\mathstrut 23q^{49} $ $\mathstrut +\mathstrut 25q^{50} $ $\mathstrut -\mathstrut 12q^{51} $ $\mathstrut +\mathstrut 7q^{52} $ $\mathstrut -\mathstrut 2q^{53} $ $\mathstrut +\mathstrut 36q^{54} $ $\mathstrut -\mathstrut 6q^{56} $ $\mathstrut +\mathstrut 52q^{57} $ $\mathstrut +\mathstrut 18q^{58} $ $\mathstrut -\mathstrut 6q^{59} $ $\mathstrut +\mathstrut 2q^{61} $ $\mathstrut +\mathstrut 28q^{62} $ $\mathstrut +\mathstrut 33q^{64} $ $\mathstrut +\mathstrut 2q^{65} $ $\mathstrut +\mathstrut 2q^{66} $ $\mathstrut +\mathstrut 10q^{67} $ $\mathstrut +\mathstrut 2q^{68} $ $\mathstrut -\mathstrut 14q^{69} $ $\mathstrut +\mathstrut 4q^{70} $ $\mathstrut -\mathstrut 38q^{71} $ $\mathstrut -\mathstrut q^{72} $ $\mathstrut +\mathstrut 38q^{73} $ $\mathstrut +\mathstrut 50q^{74} $ $\mathstrut -\mathstrut 28q^{75} $ $\mathstrut -\mathstrut 36q^{76} $ $\mathstrut +\mathstrut 4q^{77} $ $\mathstrut -\mathstrut 2q^{78} $ $\mathstrut +\mathstrut 12q^{79} $ $\mathstrut +\mathstrut 26q^{80} $ $\mathstrut +\mathstrut 3q^{81} $ $\mathstrut +\mathstrut 18q^{82} $ $\mathstrut -\mathstrut 28q^{83} $ $\mathstrut +\mathstrut 44q^{84} $ $\mathstrut +\mathstrut 40q^{85} $ $\mathstrut -\mathstrut 8q^{86} $ $\mathstrut -\mathstrut 20q^{87} $ $\mathstrut +\mathstrut 15q^{88} $ $\mathstrut -\mathstrut 20q^{89} $ $\mathstrut +\mathstrut 14q^{90} $ $\mathstrut +\mathstrut 86q^{92} $ $\mathstrut +\mathstrut 2q^{93} $ $\mathstrut +\mathstrut 32q^{94} $ $\mathstrut -\mathstrut 52q^{95} $ $\mathstrut -\mathstrut 64q^{96} $ $\mathstrut +\mathstrut 36q^{97} $ $\mathstrut -\mathstrut 17q^{98} $ $\mathstrut -\mathstrut 9q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(143))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	11	13	$q$-expansion
143.2.a.a	$1$	$1.142$	$\Q$	None	$0$	$-1$	$-1$	$-2$	$+$	$+$	$q-q^{3}-2q^{4}-q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots$
143.2.a.b	$4$	$1.142$	4.4.1957.1	None	$3$	$0$	$0$	$6$	$-$	$+$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots$
143.2.a.c	$6$	$1.142$	6.6.194616205.1	None	$0$	$3$	$1$	$4$	$+$	$-$	$q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(143))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(143)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(11))$$^{\oplus 2}$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	143.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 3 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

\(11\)	\(13\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(1\)
\(+\)	\(-\)	\(-\)	\(6\)
\(-\)	\(+\)	\(-\)	\(4\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(10\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	11	13	$q$-expansion
143.2.a.a	\(1\)	\(1.142\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-2\)	\(+\)	\(+\)	\(q-q^{3}-2q^{4}-q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots\)
143.2.a.b	\(4\)	\(1.142\)	4.4.1957.1	None	\(3\)	\(0\)	\(0\)	\(6\)	\(-\)	\(+\)	\(q+(1+\beta _{1}+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\)
143.2.a.c	\(6\)	\(1.142\)	6.6.194616205.1	None	\(0\)	\(3\)	\(1\)	\(4\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

Introduction and more

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(143))\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(143))\) into lower level spaces

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	143.2.a

Level	143
Weight	2
Character orbit	a
Rep. character	\(\chi_{143}(1,\cdot)\)
Character field	\(\Q\)
Dimension	11
Newforms	3
Sturm bound	28
Trace bound	1