Space of modular forms of level 1045, weight 6, and trivial character

• Label: 1045.6.a
• Level: $1045$
• Weight: $6$
• Character orbit: 1045.a
• Rep. character: $\chi_{1045}(1,\cdot)$
• Character field: $\Q$
• Dimension: $300$
• Newform subspaces: $8$
• Sturm bound: $720$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(720\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(1045))\).

	Total	New	Old
Modular forms	604	300	304
Cusp forms	596	300	296
Eisenstein series	8	0	8

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

\(5\)	\(11\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(37\)
\(+\)	\(+\)	\(-\)	$-$	\(39\)
\(+\)	\(-\)	\(+\)	$-$	\(37\)
\(+\)	\(-\)	\(-\)	$+$	\(35\)
\(-\)	\(+\)	\(+\)	$-$	\(38\)
\(-\)	\(+\)	\(-\)	$+$	\(36\)
\(-\)	\(-\)	\(+\)	$+$	\(38\)
\(-\)	\(-\)	\(-\)	$-$	\(40\)
Plus space			\(+\)	\(146\)
Minus space			\(-\)	\(154\)

Trace form

\( 300 q + 4800 q^{4} + 100 q^{5} + 296 q^{6} - 1704 q^{8} + 23540 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(1045))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	11	19
1045.6.a.a	$1045$	$6$	1045.a	1.a	$1$	$35$	$35$	$167.601$		None	✓	$1$	$1$	\(-4\)	\(-27\)	\(-875\)	\(117\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
1045.6.a.b	$1045$	$6$	1045.a	1.a	$1$	$36$	$36$	$167.601$		None	✓	$1$	$1$	\(-8\)	\(-63\)	\(900\)	\(-509\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
1045.6.a.c	$1045$	$6$	1045.a	1.a	$1$	$37$	$37$	$167.601$		None	✓	$1$	$1$	\(-12\)	\(-27\)	\(-925\)	\(337\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
1045.6.a.d	$1045$	$6$	1045.a	1.a	$1$	$37$	$37$	$167.601$		None	✓	$1$	$0$	\(4\)	\(27\)	\(-925\)	\(-79\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
1045.6.a.e	$1045$	$6$	1045.a	1.a	$1$	$38$	$38$	$167.601$		None	✓	$1$	$1$	\(-24\)	\(-63\)	\(950\)	\(-729\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
1045.6.a.f	$1045$	$6$	1045.a	1.a	$1$	$38$	$38$	$167.601$		None	✓	$1$	$0$	\(8\)	\(63\)	\(950\)	\(275\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
1045.6.a.g	$1045$	$6$	1045.a	1.a	$1$	$39$	$39$	$167.601$		None	✓	$1$	$0$	\(12\)	\(27\)	\(-975\)	\(-251\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
1045.6.a.h	$1045$	$6$	1045.a	1.a	$1$	$40$	$40$	$167.601$		None	✓	$1$	$0$	\(24\)	\(63\)	\(1000\)	\(839\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(1045))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(1045)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 2}\)