Space of modular forms of level 507, weight 2, and Character 507.p

• Label: 507.2.p
• Level: $507$
• Weight: $2$
• Character orbit: 507.p
• Rep. character: $\chi_{507}(25,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $360$
• Newform subspaces: $2$
• Sturm bound: $121$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(121\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(507, [\chi])\).

	Total	New	Old
Modular forms	744	360	384
Cusp forms	696	360	336
Eisenstein series	48	0	48

Trace form

360 * q + 2 * q^3 + 30 * q^4 - 30 * q^9 - 4 * q^10 - 6 * q^12 - 50 * q^13 - 8 * q^14 - 14 * q^16 + 8 * q^17 - 56 * q^22 - 4 * q^23 + 14 * q^25 + 12 * q^26 + 2 * q^27 - 4 * q^29 - 4 * q^30 - 52 * q^31 + 130 * q^32 - 130 * q^34 + 4 * q^35 + 30 * q^36 + 138 * q^38 - 2 * q^39 + 12 * q^40 - 118 * q^42 - 4 * q^43 - 2 * q^48 - 126 * q^49 - 16 * q^51 + 128 * q^52 - 74 * q^53 + 90 * q^55 - 24 * q^56 - 52 * q^58 - 208 * q^59 + 104 * q^60 + 20 * q^61 + 102 * q^62 + 10 * q^64 - 88 * q^66 + 52 * q^67 - 118 * q^68 - 4 * q^69 - 78 * q^71 + 88 * q^74 + 2 * q^75 - 260 * q^76 + 8 * q^77 + 118 * q^78 + 28 * q^79 - 30 * q^81 + 86 * q^82 + 78 * q^85 + 156 * q^86 - 88 * q^87 - 296 * q^88 - 4 * q^90 - 128 * q^91 + 28 * q^92 - 130 * q^93 + 50 * q^94 - 124 * q^95 + 156 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(507, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
507.2.p.a	$507$	$2$	507.p	169.h	$26$	$168$	$14$	$4.048$		None		✓			507.2.p.a	$2$	$0$	\(0\)	\(-14\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{26}]$
507.2.p.b	$507$	$2$	507.p	169.h	$26$	$192$	$16$	$4.048$		None		✓	✓		507.2.p.b	$2$	$0$	\(0\)	\(16\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{26}]$

Decomposition of \(S_{2}^{\mathrm{old}}(507, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(507, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)