LMFDB - Space of Modular Forms of Level 8023, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	8023.a (trivial)
Character field:			$\Q$
Newforms:			$ 5 $
Sturm bound:			$1368$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8023))$.

	Total	New	Old
Modular forms	686	653	33
Cusp forms	683	653	30
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.

$71$	$113$	Fricke	Dim.
$+$	$+$	$+$	$161$
$+$	$-$	$-$	$172$
$-$	$+$	$-$	$165$
$-$	$-$	$+$	$155$
Plus space		$+$	$316$
Minus space		$-$	$337$

Trace form

$653q $ $\mathstrut +\mathstrut 3q^{2} $ $\mathstrut +\mathstrut 655q^{4} $ $\mathstrut -\mathstrut 2q^{5} $ $\mathstrut -\mathstrut 16q^{7} $ $\mathstrut +\mathstrut 15q^{8} $ $\mathstrut +\mathstrut 653q^{9} $ $\mathstrut +\mathstrut 6q^{10} $ $\mathstrut -\mathstrut 4q^{11} $ $\mathstrut +\mathstrut 16q^{12} $ $\mathstrut -\mathstrut 10q^{13} $ $\mathstrut +\mathstrut 8q^{14} $ $\mathstrut +\mathstrut 16q^{15} $ $\mathstrut +\mathstrut 671q^{16} $ $\mathstrut +\mathstrut 10q^{17} $ $\mathstrut +\mathstrut 25q^{18} $ $\mathstrut -\mathstrut 16q^{19} $ $\mathstrut -\mathstrut 20q^{20} $ $\mathstrut -\mathstrut 24q^{21} $ $\mathstrut +\mathstrut 8q^{22} $ $\mathstrut +\mathstrut 4q^{23} $ $\mathstrut +\mathstrut 10q^{24} $ $\mathstrut +\mathstrut 647q^{25} $ $\mathstrut -\mathstrut 6q^{26} $ $\mathstrut +\mathstrut 12q^{27} $ $\mathstrut -\mathstrut 44q^{28} $ $\mathstrut -\mathstrut 18q^{29} $ $\mathstrut -\mathstrut 14q^{30} $ $\mathstrut -\mathstrut 12q^{31} $ $\mathstrut -\mathstrut 17q^{32} $ $\mathstrut -\mathstrut 12q^{33} $ $\mathstrut +\mathstrut 54q^{34} $ $\mathstrut +\mathstrut 20q^{35} $ $\mathstrut +\mathstrut 659q^{36} $ $\mathstrut +\mathstrut 6q^{37} $ $\mathstrut -\mathstrut 46q^{38} $ $\mathstrut -\mathstrut 4q^{39} $ $\mathstrut +\mathstrut 6q^{40} $ $\mathstrut -\mathstrut 2q^{41} $ $\mathstrut -\mathstrut 20q^{42} $ $\mathstrut -\mathstrut 16q^{43} $ $\mathstrut -\mathstrut 44q^{44} $ $\mathstrut -\mathstrut 22q^{45} $ $\mathstrut +\mathstrut 12q^{46} $ $\mathstrut -\mathstrut 36q^{47} $ $\mathstrut -\mathstrut 14q^{48} $ $\mathstrut +\mathstrut 557q^{49} $ $\mathstrut -\mathstrut 83q^{50} $ $\mathstrut +\mathstrut 52q^{51} $ $\mathstrut -\mathstrut 10q^{52} $ $\mathstrut +\mathstrut 34q^{53} $ $\mathstrut -\mathstrut 72q^{54} $ $\mathstrut -\mathstrut 4q^{55} $ $\mathstrut -\mathstrut 12q^{56} $ $\mathstrut +\mathstrut 8q^{57} $ $\mathstrut -\mathstrut 50q^{58} $ $\mathstrut +\mathstrut 20q^{59} $ $\mathstrut -\mathstrut 10q^{60} $ $\mathstrut -\mathstrut 6q^{61} $ $\mathstrut -\mathstrut 48q^{62} $ $\mathstrut -\mathstrut 16q^{63} $ $\mathstrut +\mathstrut 703q^{64} $ $\mathstrut +\mathstrut 16q^{65} $ $\mathstrut +\mathstrut 92q^{66} $ $\mathstrut +\mathstrut 16q^{67} $ $\mathstrut -\mathstrut 130q^{68} $ $\mathstrut +\mathstrut 52q^{69} $ $\mathstrut -\mathstrut 48q^{70} $ $\mathstrut -\mathstrut 13q^{71} $ $\mathstrut +\mathstrut 31q^{72} $ $\mathstrut -\mathstrut 34q^{73} $ $\mathstrut -\mathstrut 20q^{74} $ $\mathstrut -\mathstrut 24q^{75} $ $\mathstrut -\mathstrut 24q^{76} $ $\mathstrut -\mathstrut 4q^{77} $ $\mathstrut -\mathstrut 48q^{78} $ $\mathstrut -\mathstrut 40q^{79} $ $\mathstrut -\mathstrut 58q^{80} $ $\mathstrut +\mathstrut 645q^{81} $ $\mathstrut +\mathstrut 42q^{82} $ $\mathstrut -\mathstrut 36q^{83} $ $\mathstrut -\mathstrut 20q^{84} $ $\mathstrut +\mathstrut 48q^{85} $ $\mathstrut -\mathstrut 24q^{86} $ $\mathstrut -\mathstrut 32q^{87} $ $\mathstrut -\mathstrut 24q^{88} $ $\mathstrut -\mathstrut 38q^{89} $ $\mathstrut -\mathstrut 88q^{90} $ $\mathstrut -\mathstrut 40q^{91} $ $\mathstrut -\mathstrut 20q^{92} $ $\mathstrut +\mathstrut 16q^{93} $ $\mathstrut -\mathstrut 4q^{94} $ $\mathstrut -\mathstrut 8q^{95} $ $\mathstrut +\mathstrut 12q^{96} $ $\mathstrut -\mathstrut 42q^{97} $ $\mathstrut -\mathstrut 29q^{98} $ $\mathstrut +\mathstrut 24q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8023))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	71	113	$q$-expansion
8023.2.a.a	$3$	$64.064$	$\Q(\zeta_{14})^+$	None	$2$	$3$	$-1$	$-2$	$+$	$+$	$q+(1-\beta _{1})q^{2}+(2\beta _{1}-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
8023.2.a.b	$155$	$64.064$		None	$-21$	$-16$	$-26$	$-40$	$-$	$-$
8023.2.a.c	$158$	$64.064$		None	$-24$	$-23$	$-31$	$-2$	$+$	$+$
8023.2.a.d	$165$	$64.064$		None	$22$	$18$	$28$	$24$	$-$	$+$
8023.2.a.e	$172$	$64.064$		None	$24$	$18$	$28$	$4$	$+$	$-$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8023))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(8023)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(71))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(113))$$^{\oplus 2}$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	8023.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 5 \)
Sturm bound:			\(1368\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

\(71\)	\(113\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(161\)
\(+\)	\(-\)	\(-\)	\(172\)
\(-\)	\(+\)	\(-\)	\(165\)
\(-\)	\(-\)	\(+\)	\(155\)
Plus space		\(+\)	\(316\)
Minus space		\(-\)	\(337\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	71	113	$q$-expansion
8023.2.a.a	\(3\)	\(64.064\)	\(\Q(\zeta_{14})^+\)	None	\(2\)	\(3\)	\(-1\)	\(-2\)	\(+\)	\(+\)	\(q+(1-\beta _{1})q^{2}+(2\beta _{1}-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
8023.2.a.b	\(155\)	\(64.064\)		None	\(-21\)	\(-16\)	\(-26\)	\(-40\)	\(-\)	\(-\)
8023.2.a.c	\(158\)	\(64.064\)		None	\(-24\)	\(-23\)	\(-31\)	\(-2\)	\(+\)	\(+\)
8023.2.a.d	\(165\)	\(64.064\)		None	\(22\)	\(18\)	\(28\)	\(24\)	\(-\)	\(+\)
8023.2.a.e	\(172\)	\(64.064\)		None	\(24\)	\(18\)	\(28\)	\(4\)	\(+\)	\(-\)

Introduction and more

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8023))\) 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	8023.2.a

Level	8023
Weight	2
Character orbit	a
Rep. character	\(\chi_{8023}(1,\cdot)\)
Character field	\(\Q\)
Dimension	653
Newforms	5
Sturm bound	1368
Trace bound	1