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

• Label: 522.2.n
• Level: $522$
• Weight: $2$
• Character orbit: 522.n
• Rep. character: $\chi_{522}(91,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $180$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	522.n (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(180\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	588	72	516
Cusp forms	492	72	420
Eisenstein series	96	0	96

Trace form

72 * q + 12 * q^4 + 2 * q^5 - 4 * q^7 + 18 * q^13 - 12 * q^16 - 2 * q^20 + 12 * q^22 + 44 * q^23 + 12 * q^25 + 14 * q^26 + 4 * q^28 + 18 * q^29 + 28 * q^31 + 6 * q^34 + 36 * q^35 - 28 * q^37 + 22 * q^38 + 28 * q^43 + 28 * q^44 - 14 * q^47 - 50 * q^49 - 28 * q^50 + 10 * q^52 + 34 * q^53 + 56 * q^55 - 32 * q^58 + 64 * q^59 + 28 * q^61 + 2 * q^62 + 12 * q^64 - 2 * q^65 - 24 * q^67 - 14 * q^68 - 94 * q^71 - 28 * q^73 + 2 * q^74 - 28 * q^76 - 126 * q^77 - 28 * q^79 + 2 * q^80 - 28 * q^83 - 28 * q^85 - 60 * q^86 - 12 * q^88 - 42 * q^89 - 140 * q^91 - 44 * q^92 - 48 * q^94 - 70 * q^97 - 112 * q^98

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.n.a	$522$	$2$	522.n	29.e	$14$	$12$	$2$	$4.168$	\(\Q(\zeta_{28})\)	None					58.2.e.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q-\zeta_{28}^{9}q^{2}-\zeta_{28}^{4}q^{4}+(\zeta_{28}+\zeta_{28}^{2}+\cdots)q^{5}+\cdots\)
522.2.n.b	$522$	$2$	522.n	29.e	$14$	$12$	$2$	$4.168$	\(\Q(\zeta_{28})\)	None					174.2.h.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q-\zeta_{28}^{9}q^{2}-\zeta_{28}^{4}q^{4}+(-\zeta_{28}+\zeta_{28}^{2}+\cdots)q^{5}+\cdots\)
522.2.n.c	$522$	$2$	522.n	29.e	$14$	$24$	$4$	$4.168$		None					174.2.h.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-12\)		$\mathrm{SU}(2)[C_{14}]$
522.2.n.d	$522$	$2$	522.n	29.e	$14$	$24$	$4$	$4.168$		None		✓			522.2.n.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{14}]$

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

\( S_{2}^{\mathrm{old}}(522, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)