Space of modular forms of level 8019, weight 2, and trivial character

• Label: 8019.2.a
• Level: $8019$
• Weight: $2$
• Character orbit: 8019.a
• Rep. character: $\chi_{8019}(1,\cdot)$
• Character field: $\Q$
• Dimension: $360$
• Newform subspaces: $12$
• Sturm bound: $1944$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 8019 = 3^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8019.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1944\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8019))\).

	Total	New	Old
Modular forms	1008	360	648
Cusp forms	937	360	577
Eisenstein series	71	0	71

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

\(3\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(87\)
\(+\)	\(-\)	$-$	\(99\)
\(-\)	\(+\)	$-$	\(93\)
\(-\)	\(-\)	$+$	\(81\)
Plus space		\(+\)	\(168\)
Minus space		\(-\)	\(192\)

Trace form

\( 360 q + 360 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	11
8019.2.a.a	$8019$	$2$	8019.a	1.a	$1$	$3$	$3$	$64.032$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}-2\beta _{2})q^{5}+\cdots\)
8019.2.a.b	$8019$	$2$	8019.a	1.a	$1$	$3$	$3$	$64.032$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
8019.2.a.c	$8019$	$2$	8019.a	1.a	$1$	$21$	$21$	$64.032$		None	✓	$1$	$1$	\(-6\)	\(0\)	\(-12\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8019.2.a.d	$8019$	$2$	8019.a	1.a	$1$	$21$	$21$	$64.032$		None	✓	$1$	$1$	\(0\)	\(0\)	\(-12\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8019.2.a.e	$8019$	$2$	8019.a	1.a	$1$	$21$	$21$	$64.032$		None	✓	$1$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8019.2.a.f	$8019$	$2$	8019.a	1.a	$1$	$21$	$21$	$64.032$		None	✓	$1$	$0$	\(6\)	\(0\)	\(12\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8019.2.a.g	$8019$	$2$	8019.a	1.a	$1$	$36$	$36$	$64.032$		None	✓	$1$	$1$	\(0\)	\(0\)	\(-9\)	\(-9\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8019.2.a.h	$8019$	$2$	8019.a	1.a	$1$	$36$	$36$	$64.032$		None	✓	$1$	$1$	\(0\)	\(0\)	\(9\)	\(-9\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8019.2.a.i	$8019$	$2$	8019.a	1.a	$1$	$48$	$48$	$64.032$		None	✓	$1$	$1$	\(-6\)	\(0\)	\(-24\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
8019.2.a.j	$8019$	$2$	8019.a	1.a	$1$	$48$	$48$	$64.032$		None	✓	$1$	$0$	\(6\)	\(0\)	\(24\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
8019.2.a.k	$8019$	$2$	8019.a	1.a	$1$	$51$	$51$	$64.032$		None	✓	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(12\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
8019.2.a.l	$8019$	$2$	8019.a	1.a	$1$	$51$	$51$	$64.032$		None	✓	$1$	$0$	\(0\)	\(0\)	\(6\)	\(12\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8019))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8019)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(729))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(891))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2673))\)\(^{\oplus 2}\)