Space of modular forms of level 1028, weight 6, and trivial character

• Label: 1028.6.a
• Level: $1028$
• Weight: $6$
• Character orbit: 1028.a
• Rep. character: $\chi_{1028}(1,\cdot)$
• Character field: $\Q$
• Dimension: $106$
• Newform subspaces: $2$
• Sturm bound: $774$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1028 = 2^{2} \cdot 257 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1028.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(774\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(1028))\).

	Total	New	Old
Modular forms	648	106	542
Cusp forms	642	106	536
Eisenstein series	6	0	6

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

\(2\)	\(257\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(57\)
\(-\)	\(-\)	$+$	\(49\)
Plus space		\(+\)	\(49\)
Minus space		\(-\)	\(57\)

Trace form

\( 106 q - 28 q^{5} + 176 q^{7} + 8804 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(1028))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	257
1028.6.a.a	$1028$	$6$	1028.a	1.a	$1$	$49$	$49$	$164.875$		None	✓	$1$	$1$	\(0\)	\(-27\)	\(-89\)	\(88\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
1028.6.a.b	$1028$	$6$	1028.a	1.a	$1$	$57$	$57$	$164.875$		None	✓	$1$	$0$	\(0\)	\(27\)	\(61\)	\(88\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(1028))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(1028)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(257))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(514))\)\(^{\oplus 2}\)