Space of modular forms of level 4028, weight 2, and Character 4028.c

• Label: 4028.2.c
• Level: $4028$
• Weight: $2$
• Character orbit: 4028.c
• Rep. character: $\chi_{4028}(3497,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $1$
• Sturm bound: $1080$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4028.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1080\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4028, [\chi])\).

	Total	New	Old
Modular forms	546	82	464
Cusp forms	534	82	452
Eisenstein series	12	0	12

Trace form

82 * q - 8 * q^7 - 82 * q^9 + 4 * q^13 + 4 * q^15 - 4 * q^17 - 58 * q^25 - 16 * q^29 - 12 * q^37 - 32 * q^43 + 8 * q^47 + 98 * q^49 + 6 * q^53 - 4 * q^57 + 4 * q^59 + 8 * q^63 + 28 * q^69 - 8 * q^77 + 154 * q^81 - 20 * q^89 + 48 * q^91 - 56 * q^93 - 44 * q^97 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(4028, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4028.2.c.a	$4028$	$2$	4028.c	53.b	$2$	$82$	$82$	$32.164$		None		✓	✓	✓	4028.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4028, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4028, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(106, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(212, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1007, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2014, [\chi])\)\(^{\oplus 2}\)