Space of modular forms of level 6021, weight 2, and trivial character

• Label: 6021.2.a
• Level: $6021$
• Weight: $2$
• Character orbit: 6021.a
• Rep. character: $\chi_{6021}(1,\cdot)$
• Character field: $\Q$
• Dimension: $296$
• Newform subspaces: $20$
• Sturm bound: $1344$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 6021 = 3^{3} \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6021.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(1344\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6021))\).

	Total	New	Old
Modular forms	678	296	382
Cusp forms	667	296	371
Eisenstein series	11	0	11

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

\(3\)	\(223\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(71\)
\(+\)	\(-\)	$-$	\(77\)
\(-\)	\(+\)	$-$	\(77\)
\(-\)	\(-\)	$+$	\(71\)
Plus space		\(+\)	\(142\)
Minus space		\(-\)	\(154\)

Trace form

\( 296 q + 300 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6021))\) 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	223
6021.2.a.a	$6021$	$2$	6021.a	1.a	$1$	$1$	$1$	$48.078$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{7}-q^{13}+2q^{14}+\cdots\)
6021.2.a.b	$6021$	$2$	6021.a	1.a	$1$	$1$	$1$	$48.078$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+3q^{5}+q^{7}-6q^{10}+\cdots\)
6021.2.a.c	$6021$	$2$	6021.a	1.a	$1$	$1$	$1$	$48.078$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{5}-2q^{7}+3q^{8}-3q^{10}+\cdots\)
6021.2.a.d	$6021$	$2$	6021.a	1.a	$1$	$1$	$1$	$48.078$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-3q^{5}-3q^{7}+4q^{11}-2q^{13}+\cdots\)
6021.2.a.e	$6021$	$2$	6021.a	1.a	$1$	$1$	$1$	$48.078$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}-3q^{7}-4q^{11}-2q^{13}+\cdots\)
6021.2.a.f	$6021$	$2$	6021.a	1.a	$1$	$1$	$1$	$48.078$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{5}-2q^{7}-3q^{8}-3q^{10}+\cdots\)
6021.2.a.g	$6021$	$2$	6021.a	1.a	$1$	$1$	$1$	$48.078$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-3q^{5}+q^{7}-6q^{10}+\cdots\)
6021.2.a.h	$6021$	$2$	6021.a	1.a	$1$	$1$	$1$	$48.078$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{7}-q^{13}-2q^{14}+\cdots\)
6021.2.a.i	$6021$	$2$	6021.a	1.a	$1$	$2$	$2$	$48.078$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+2\beta )q^{5}+q^{7}-2\beta q^{8}+\cdots\)
6021.2.a.j	$6021$	$2$	6021.a	1.a	$1$	$2$	$2$	$48.078$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+2\beta )q^{5}+q^{7}-2\beta q^{8}+\cdots\)
6021.2.a.k	$6021$	$2$	6021.a	1.a	$1$	$4$	$4$	$48.078$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-2\beta _{2}q^{8}+\cdots\)
6021.2.a.l	$6021$	$2$	6021.a	1.a	$1$	$10$	$10$	$48.078$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{3}+\beta _{6}+\beta _{8})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots\)
6021.2.a.m	$6021$	$2$	6021.a	1.a	$1$	$30$	$30$	$48.078$		None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-10\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6021.2.a.n	$6021$	$2$	6021.a	1.a	$1$	$30$	$30$	$48.078$		None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(14\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6021.2.a.o	$6021$	$2$	6021.a	1.a	$1$	$30$	$30$	$48.078$		None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-20\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6021.2.a.p	$6021$	$2$	6021.a	1.a	$1$	$35$	$35$	$48.078$		None	✓	$1$	$1$	\(-4\)	\(0\)	\(-14\)	\(2\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6021.2.a.q	$6021$	$2$	6021.a	1.a	$1$	$35$	$35$	$48.078$		None	✓	$1$	$1$	\(-4\)	\(0\)	\(-10\)	\(-2\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6021.2.a.r	$6021$	$2$	6021.a	1.a	$1$	$35$	$35$	$48.078$		None	✓	$1$	$0$	\(4\)	\(0\)	\(10\)	\(-2\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6021.2.a.s	$6021$	$2$	6021.a	1.a	$1$	$35$	$35$	$48.078$		None	✓	$1$	$0$	\(4\)	\(0\)	\(14\)	\(2\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6021.2.a.t	$6021$	$2$	6021.a	1.a	$1$	$40$	$40$	$48.078$		None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6021))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6021)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(669))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2007))\)\(^{\oplus 2}\)