LMFDB - Space of Modular Forms of Level 8013, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	8013.a (trivial)
Character field:			$\Q$
Newforms:			$ 4 $
Sturm bound:			$1781$
Trace bound:			$1$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8013))$.

	Total	New	Old
Modular forms	892	445	447
Cusp forms	889	445	444
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.

$3$	$2671$	Fricke	Dim.
$+$	$+$	$+$	$116$
$+$	$-$	$-$	$106$
$-$	$+$	$-$	$129$
$-$	$-$	$+$	$94$
Plus space		$+$	$210$
Minus space		$-$	$235$

Trace form

$445q $ $\mathstrut +\mathstrut q^{2} $ $\mathstrut +\mathstrut q^{3} $ $\mathstrut +\mathstrut 449q^{4} $ $\mathstrut -\mathstrut 2q^{5} $ $\mathstrut +\mathstrut 3q^{6} $ $\mathstrut +\mathstrut 8q^{7} $ $\mathstrut +\mathstrut 9q^{8} $ $\mathstrut +\mathstrut 445q^{9} $ $\mathstrut +\mathstrut 2q^{10} $ $\mathstrut -\mathstrut q^{12} $ $\mathstrut +\mathstrut 2q^{13} $ $\mathstrut +\mathstrut 16q^{14} $ $\mathstrut +\mathstrut 6q^{15} $ $\mathstrut +\mathstrut 461q^{16} $ $\mathstrut -\mathstrut 6q^{17} $ $\mathstrut +\mathstrut q^{18} $ $\mathstrut +\mathstrut 8q^{19} $ $\mathstrut +\mathstrut 22q^{20} $ $\mathstrut +\mathstrut 4q^{21} $ $\mathstrut +\mathstrut 8q^{22} $ $\mathstrut +\mathstrut 8q^{23} $ $\mathstrut +\mathstrut 3q^{24} $ $\mathstrut +\mathstrut 439q^{25} $ $\mathstrut +\mathstrut 2q^{26} $ $\mathstrut +\mathstrut q^{27} $ $\mathstrut +\mathstrut 24q^{28} $ $\mathstrut +\mathstrut 2q^{29} $ $\mathstrut +\mathstrut 2q^{30} $ $\mathstrut +\mathstrut 24q^{31} $ $\mathstrut +\mathstrut 29q^{32} $ $\mathstrut +\mathstrut 4q^{33} $ $\mathstrut +\mathstrut 14q^{34} $ $\mathstrut +\mathstrut 16q^{35} $ $\mathstrut +\mathstrut 449q^{36} $ $\mathstrut +\mathstrut 2q^{37} $ $\mathstrut -\mathstrut 12q^{38} $ $\mathstrut +\mathstrut 6q^{39} $ $\mathstrut -\mathstrut 6q^{40} $ $\mathstrut -\mathstrut 22q^{41} $ $\mathstrut -\mathstrut 20q^{42} $ $\mathstrut -\mathstrut 20q^{43} $ $\mathstrut +\mathstrut 16q^{44} $ $\mathstrut -\mathstrut 2q^{45} $ $\mathstrut +\mathstrut 24q^{47} $ $\mathstrut +\mathstrut 15q^{48} $ $\mathstrut +\mathstrut 453q^{49} $ $\mathstrut -\mathstrut 17q^{50} $ $\mathstrut -\mathstrut 2q^{51} $ $\mathstrut -\mathstrut 14q^{52} $ $\mathstrut +\mathstrut 6q^{53} $ $\mathstrut +\mathstrut 3q^{54} $ $\mathstrut +\mathstrut 40q^{55} $ $\mathstrut +\mathstrut 40q^{56} $ $\mathstrut +\mathstrut 18q^{58} $ $\mathstrut +\mathstrut 8q^{59} $ $\mathstrut +\mathstrut 22q^{60} $ $\mathstrut -\mathstrut 6q^{61} $ $\mathstrut +\mathstrut 4q^{62} $ $\mathstrut +\mathstrut 8q^{63} $ $\mathstrut +\mathstrut 505q^{64} $ $\mathstrut -\mathstrut 44q^{65} $ $\mathstrut +\mathstrut 12q^{66} $ $\mathstrut +\mathstrut 24q^{67} $ $\mathstrut -\mathstrut 58q^{68} $ $\mathstrut -\mathstrut 36q^{70} $ $\mathstrut +\mathstrut 32q^{71} $ $\mathstrut +\mathstrut 9q^{72} $ $\mathstrut -\mathstrut 18q^{73} $ $\mathstrut +\mathstrut 10q^{74} $ $\mathstrut -\mathstrut 17q^{75} $ $\mathstrut +\mathstrut 100q^{76} $ $\mathstrut +\mathstrut 60q^{77} $ $\mathstrut +\mathstrut 2q^{78} $ $\mathstrut +\mathstrut 24q^{79} $ $\mathstrut -\mathstrut 6q^{80} $ $\mathstrut +\mathstrut 445q^{81} $ $\mathstrut -\mathstrut 54q^{82} $ $\mathstrut +\mathstrut 20q^{83} $ $\mathstrut +\mathstrut 20q^{84} $ $\mathstrut -\mathstrut 8q^{85} $ $\mathstrut +\mathstrut 44q^{86} $ $\mathstrut +\mathstrut 6q^{87} $ $\mathstrut +\mathstrut 40q^{88} $ $\mathstrut -\mathstrut 30q^{89} $ $\mathstrut +\mathstrut 2q^{90} $ $\mathstrut -\mathstrut 4q^{91} $ $\mathstrut +\mathstrut 4q^{92} $ $\mathstrut -\mathstrut 12q^{93} $ $\mathstrut +\mathstrut 8q^{95} $ $\mathstrut +\mathstrut 19q^{96} $ $\mathstrut +\mathstrut 14q^{97} $ $\mathstrut +\mathstrut 41q^{98} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8013))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	3	2671	$q$-expansion
8013.2.a.a	$94$	$63.984$		None	$-13$	$94$	$-14$	$-55$	$-$	$-$
8013.2.a.b	$106$	$63.984$		None	$15$	$-106$	$16$	$35$	$+$	$-$
8013.2.a.c	$116$	$63.984$		None	$-16$	$-116$	$-20$	$-33$	$+$	$+$
8013.2.a.d	$129$	$63.984$		None	$15$	$129$	$16$	$61$	$-$	$+$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8013))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(8013)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(2671))$$^{\oplus 2}$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	8013.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 4 \)
Sturm bound:			\(1781\)
Trace bound:			\(1\)

\(3\)	\(2671\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(116\)
\(+\)	\(-\)	\(-\)	\(106\)
\(-\)	\(+\)	\(-\)	\(129\)
\(-\)	\(-\)	\(+\)	\(94\)
Plus space		\(+\)	\(210\)
Minus space		\(-\)	\(235\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs		$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	3	2671	$q$-expansion
8013.2.a.a	\(94\)	\(63.984\)		None	\(-13\)	\(94\)	\(-14\)	\(-55\)	\(-\)	\(-\)
8013.2.a.b	\(106\)	\(63.984\)		None	\(15\)	\(-106\)	\(16\)	\(35\)	\(+\)	\(-\)
8013.2.a.c	\(116\)	\(63.984\)		None	\(-16\)	\(-116\)	\(-20\)	\(-33\)	\(+\)	\(+\)
8013.2.a.d	\(129\)	\(63.984\)		None	\(15\)	\(129\)	\(16\)	\(61\)	\(-\)	\(+\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

Related objects

Downloads

Learn more about

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8013))\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8013))\) 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	8013.2.a

Level	8013
Weight	2
Character orbit	a
Rep. character	\(\chi_{8013}(1,\cdot)\)
Character field	\(\Q\)
Dimension	445
Newforms	4
Sturm bound	1781
Trace bound	1