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

• Label: 522.2.l
• Level: $522$
• Weight: $2$
• Character orbit: 522.l
• Rep. character: $\chi_{522}(41,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $120$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	522.l (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 261 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	376	120	256
Cusp forms	344	120	224
Eisenstein series	32	0	32

Trace form

120 * q - 24 * q^11 + 12 * q^14 + 20 * q^15 + 60 * q^16 - 28 * q^21 + 8 * q^24 - 60 * q^25 - 24 * q^27 + 12 * q^29 + 12 * q^30 - 16 * q^36 + 16 * q^39 + 12 * q^41 + 104 * q^45 - 24 * q^46 + 24 * q^47 - 60 * q^49 - 16 * q^54 - 24 * q^55 - 12 * q^56 - 12 * q^58 - 120 * q^59 + 16 * q^60 + 12 * q^61 - 36 * q^65 + 48 * q^66 + 36 * q^68 - 52 * q^69 - 72 * q^74 + 44 * q^75 + 132 * q^77 - 44 * q^78 - 12 * q^79 - 8 * q^81 - 96 * q^82 + 96 * q^83 - 4 * q^84 + 48 * q^85 + 60 * q^87 - 28 * q^90 - 192 * q^95 - 24 * 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.l.a	$522$	$2$	522.l	261.l	$12$	$120$	$30$	$4.168$		None		✓	✓	✓	522.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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