Space of modular forms of level 522, weight 2, and Character 522.r

• Label: 522.2.r
• Level: $522$
• Weight: $2$
• Character orbit: 522.r
• Rep. character: $\chi_{522}(89,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $120$
• Newform subspaces: $2$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	522.r (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 87 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(522, [\chi])\).

	Total	New	Old
Modular forms	1176	120	1056
Cusp forms	984	120	864
Eisenstein series	192	0	192

Trace form

120 * q + 12 * q^10 + 20 * q^16 + 16 * q^19 - 20 * q^25 - 8 * q^31 + 4 * q^37 - 12 * q^40 - 16 * q^43 + 32 * q^46 + 44 * q^49 + 32 * q^52 + 8 * q^55 + 8 * q^58 + 44 * q^61 + 112 * q^67 - 56 * q^70 - 32 * q^73 - 96 * q^76 - 72 * q^79 - 56 * q^82 - 280 * q^85 - 336 * q^91 - 112 * q^94 - 36 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(522, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
522.2.r.a	$522$	$2$	522.r	87.k	$28$	$48$	$4$	$4.168$		None		✓			522.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{28}]$
522.2.r.b	$522$	$2$	522.r	87.k	$28$	$72$	$6$	$4.168$		None		✓	✓		522.2.r.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{28}]$

Decomposition of \(S_{2}^{\mathrm{old}}(522, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(522, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)