Space of modular forms of level 8028, weight 2, and Character 8028.h

• Label: 8028.2.h
• Level: $8028$
• Weight: $2$
• Character orbit: 8028.h
• Rep. character: $\chi_{8028}(4013,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $2688$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 8028 = 2^{2} \cdot 3^{2} \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8028.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 669 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2688\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8028, [\chi])\).

	Total	New	Old
Modular forms	1356	76	1280
Cusp forms	1332	76	1256
Eisenstein series	24	0	24

Trace form

\( 76 q + 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(8028, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8028.2.h.a	$8028$	$2$	8028.h	669.c	$2$	$76$	$76$	$64.104$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(8028, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8028, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(669, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2007, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4014, [\chi])\)\(^{\oplus 2}\)