LMFDB - Space of Modular Forms of Level 8002, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	8002.a (trivial)
Character field:			$\Q$
Newforms:			$ 7 $
Sturm bound:			$2001$
Trace bound:			$3$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8002))$.

	Total	New	Old
Modular forms	1002	333	669
Cusp forms	999	333	666
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.

$2$	$4001$	Fricke	Dim.
$+$	$+$	$+$	$89$
$+$	$-$	$-$	$77$
$-$	$+$	$-$	$95$
$-$	$-$	$+$	$72$
Plus space		$+$	$161$
Minus space		$-$	$172$

Trace form

$333q $ $\mathstrut +\mathstrut q^{2} $ $\mathstrut -\mathstrut 2q^{3} $ $\mathstrut +\mathstrut 333q^{4} $ $\mathstrut +\mathstrut 2q^{5} $ $\mathstrut +\mathstrut 2q^{6} $ $\mathstrut -\mathstrut 4q^{7} $ $\mathstrut +\mathstrut q^{8} $ $\mathstrut +\mathstrut 337q^{9} $ $\mathstrut +\mathstrut 2q^{10} $ $\mathstrut +\mathstrut 6q^{11} $ $\mathstrut -\mathstrut 2q^{12} $ $\mathstrut +\mathstrut 2q^{13} $ $\mathstrut +\mathstrut 8q^{14} $ $\mathstrut +\mathstrut 12q^{15} $ $\mathstrut +\mathstrut 333q^{16} $ $\mathstrut +\mathstrut 6q^{17} $ $\mathstrut +\mathstrut 5q^{18} $ $\mathstrut +\mathstrut 2q^{20} $ $\mathstrut +\mathstrut 8q^{21} $ $\mathstrut -\mathstrut 2q^{22} $ $\mathstrut +\mathstrut 8q^{23} $ $\mathstrut +\mathstrut 2q^{24} $ $\mathstrut +\mathstrut 331q^{25} $ $\mathstrut +\mathstrut 2q^{26} $ $\mathstrut +\mathstrut 16q^{27} $ $\mathstrut -\mathstrut 4q^{28} $ $\mathstrut +\mathstrut 18q^{29} $ $\mathstrut +\mathstrut 12q^{30} $ $\mathstrut -\mathstrut 24q^{31} $ $\mathstrut +\mathstrut q^{32} $ $\mathstrut +\mathstrut 12q^{33} $ $\mathstrut +\mathstrut 6q^{34} $ $\mathstrut +\mathstrut 337q^{36} $ $\mathstrut -\mathstrut 16q^{37} $ $\mathstrut +\mathstrut 4q^{38} $ $\mathstrut +\mathstrut 8q^{39} $ $\mathstrut +\mathstrut 2q^{40} $ $\mathstrut +\mathstrut 2q^{41} $ $\mathstrut +\mathstrut 6q^{43} $ $\mathstrut +\mathstrut 6q^{44} $ $\mathstrut +\mathstrut 2q^{45} $ $\mathstrut -\mathstrut 8q^{46} $ $\mathstrut -\mathstrut 12q^{47} $ $\mathstrut -\mathstrut 2q^{48} $ $\mathstrut +\mathstrut 337q^{49} $ $\mathstrut -\mathstrut q^{50} $ $\mathstrut +\mathstrut 28q^{51} $ $\mathstrut +\mathstrut 2q^{52} $ $\mathstrut +\mathstrut 4q^{53} $ $\mathstrut +\mathstrut 20q^{54} $ $\mathstrut -\mathstrut 4q^{55} $ $\mathstrut +\mathstrut 8q^{56} $ $\mathstrut -\mathstrut 12q^{57} $ $\mathstrut -\mathstrut 6q^{58} $ $\mathstrut +\mathstrut 12q^{59} $ $\mathstrut +\mathstrut 12q^{60} $ $\mathstrut +\mathstrut 6q^{61} $ $\mathstrut +\mathstrut 8q^{62} $ $\mathstrut -\mathstrut 8q^{63} $ $\mathstrut +\mathstrut 333q^{64} $ $\mathstrut +\mathstrut 8q^{65} $ $\mathstrut +\mathstrut 8q^{66} $ $\mathstrut -\mathstrut 10q^{67} $ $\mathstrut +\mathstrut 6q^{68} $ $\mathstrut -\mathstrut 20q^{69} $ $\mathstrut +\mathstrut 12q^{70} $ $\mathstrut -\mathstrut 4q^{71} $ $\mathstrut +\mathstrut 5q^{72} $ $\mathstrut -\mathstrut 6q^{73} $ $\mathstrut +\mathstrut 20q^{74} $ $\mathstrut -\mathstrut 54q^{75} $ $\mathstrut -\mathstrut 36q^{77} $ $\mathstrut -\mathstrut 4q^{78} $ $\mathstrut -\mathstrut 20q^{79} $ $\mathstrut +\mathstrut 2q^{80} $ $\mathstrut +\mathstrut 333q^{81} $ $\mathstrut +\mathstrut 6q^{82} $ $\mathstrut -\mathstrut 32q^{83} $ $\mathstrut +\mathstrut 8q^{84} $ $\mathstrut +\mathstrut 36q^{85} $ $\mathstrut -\mathstrut 6q^{86} $ $\mathstrut -\mathstrut 8q^{87} $ $\mathstrut -\mathstrut 2q^{88} $ $\mathstrut +\mathstrut 2q^{89} $ $\mathstrut +\mathstrut 6q^{90} $ $\mathstrut -\mathstrut 4q^{91} $ $\mathstrut +\mathstrut 8q^{92} $ $\mathstrut -\mathstrut 44q^{93} $ $\mathstrut +\mathstrut 16q^{94} $ $\mathstrut +\mathstrut 2q^{96} $ $\mathstrut +\mathstrut 14q^{97} $ $\mathstrut +\mathstrut 25q^{98} $ $\mathstrut +\mathstrut 38q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8002))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	4001	$q$-expansion
8002.2.a.a	$1$	$63.896$	$\Q$	None	$1$	$-1$	$1$	$0$	$-$	$-$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
8002.2.a.b	$1$	$63.896$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+4q^{13}+\cdots$
8002.2.a.c	$1$	$63.896$	$\Q$	None	$1$	$2$	$-2$	$0$	$-$	$-$	$q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots$
8002.2.a.d	$69$	$63.896$		None	$69$	$-25$	$-33$	$-19$	$-$	$-$
8002.2.a.e	$77$	$63.896$		None	$-77$	$10$	$18$	$21$	$+$	$-$
8002.2.a.f	$89$	$63.896$		None	$-89$	$-12$	$-18$	$-27$	$+$	$+$
8002.2.a.g	$95$	$63.896$		None	$95$	$24$	$36$	$21$	$-$	$+$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8002))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(8002)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(4001))$$^{\oplus 2}$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	8002.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 7 \)
Sturm bound:			\(2001\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

\(2\)	\(4001\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(89\)
\(+\)	\(-\)	\(-\)	\(77\)
\(-\)	\(+\)	\(-\)	\(95\)
\(-\)	\(-\)	\(+\)	\(72\)
Plus space		\(+\)	\(161\)
Minus space		\(-\)	\(172\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	4001	$q$-expansion
8002.2.a.a	\(1\)	\(63.896\)	\(\Q\)	None	\(1\)	\(-1\)	\(1\)	\(0\)	\(-\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
8002.2.a.b	\(1\)	\(63.896\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+4q^{13}+\cdots\)
8002.2.a.c	\(1\)	\(63.896\)	\(\Q\)	None	\(1\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots\)
8002.2.a.d	\(69\)	\(63.896\)		None	\(69\)	\(-25\)	\(-33\)	\(-19\)	\(-\)	\(-\)
8002.2.a.e	\(77\)	\(63.896\)		None	\(-77\)	\(10\)	\(18\)	\(21\)	\(+\)	\(-\)
8002.2.a.f	\(89\)	\(63.896\)		None	\(-89\)	\(-12\)	\(-18\)	\(-27\)	\(+\)	\(+\)
8002.2.a.g	\(95\)	\(63.896\)		None	\(95\)	\(24\)	\(36\)	\(21\)	\(-\)	\(+\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8002))\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8002))\) 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	8002.2.a

Level	8002
Weight	2
Character orbit	a
Rep. character	\(\chi_{8002}(1,\cdot)\)
Character field	\(\Q\)
Dimension	333
Newforms	7
Sturm bound	2001
Trace bound	3