Space of modular forms of level 528, weight 2, and Character 528.t

• Label: 528.2.t
• Level: $528$
• Weight: $2$
• Character orbit: 528.t
• Rep. character: $\chi_{528}(133,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.t (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(528, [\chi])\).

	Total	New	Old
Modular forms	200	80	120
Cusp forms	184	80	104
Eisenstein series	16	0	16

Trace form

80 * q + 24 * q^8 + 16 * q^10 - 16 * q^14 + 16 * q^15 + 8 * q^16 + 16 * q^19 - 16 * q^20 - 8 * q^24 - 40 * q^28 - 48 * q^31 + 40 * q^34 - 48 * q^35 + 8 * q^36 - 40 * q^38 + 8 * q^40 + 40 * q^42 + 16 * q^44 + 48 * q^46 + 32 * q^48 - 80 * q^49 - 24 * q^50 - 16 * q^51 + 72 * q^52 - 8 * q^54 + 56 * q^56 + 24 * q^58 - 32 * q^59 - 24 * q^60 - 32 * q^61 + 24 * q^62 - 24 * q^64 + 32 * q^65 + 48 * q^67 - 8 * q^68 - 32 * q^69 - 56 * q^70 - 48 * q^76 + 24 * q^78 - 32 * q^79 - 64 * q^80 - 80 * q^81 - 80 * q^82 + 32 * q^85 - 48 * q^86 + 32 * q^91 - 24 * q^92 + 16 * q^94 + 96 * q^95 - 40 * q^96 - 8 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(528, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
528.2.t.a	$528$	$2$	528.t	16.e	$4$	$40$	$20$	$4.216$		None		✓			528.2.t.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
528.2.t.b	$528$	$2$	528.t	16.e	$4$	$40$	$20$	$4.216$		None		✓			528.2.t.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(528, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)