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

• Label: 507.2.t
• Level: $507$
• Weight: $2$
• Character orbit: 507.t
• Rep. character: $\chi_{507}(4,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $696$
• 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.t (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{78})\)
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	1512	696	816
Cusp forms	1416	696	720
Eisenstein series	96	0	96

Trace form

696 * q - q^3 - 26 * q^4 + 3 * q^7 + 29 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 + 32 * q^13 + 8 * q^14 - 6 * q^15 + 28 * q^16 + 4 * q^17 - 6 * q^19 - 12 * q^20 + 44 * q^22 - 2 * q^23 + 62 * q^25 + 2 * q^27 - 6 * q^28 - 2 * q^29 + 4 * q^30 + 52 * q^31 - 130 * q^32 + 6 * q^33 + 130 * q^34 + 2 * q^35 - 26 * q^36 - 138 * q^38 - 2 * q^39 + 24 * q^40 + 12 * q^41 - 260 * q^42 + 11 * q^43 - 6 * q^45 - 12 * q^48 + 140 * q^49 - 8 * q^51 - 120 * q^52 + 86 * q^53 - 102 * q^55 + 12 * q^56 + 52 * q^58 - 410 * q^59 - 104 * q^60 - 15 * q^61 - 114 * q^62 - 3 * q^63 - 6 * q^65 + 112 * q^66 - 67 * q^67 + 106 * q^68 + 10 * q^69 - 138 * q^71 - 64 * q^74 + 15 * q^75 - 40 * q^76 - 44 * q^77 - 130 * q^78 + 46 * q^79 + 24 * q^80 + 29 * q^81 - 110 * q^82 - 6 * q^84 - 78 * q^85 - 156 * q^86 + 94 * q^87 - 496 * q^88 - 12 * q^89 - 8 * q^90 + 113 * q^91 + 80 * q^92 - 3 * q^93 - 38 * q^94 - 200 * q^95 - 147 * 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.t.a	$507$	$2$	507.t	169.k	$78$	$336$	$14$	$4.048$		None		✓			507.2.t.a	$2$	$0$	\(0\)	\(14\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{78}]$
507.2.t.b	$507$	$2$	507.t	169.k	$78$	$360$	$15$	$4.048$		None		✓	✓		507.2.t.b	$2$	$0$	\(0\)	\(-15\)	\(0\)	\(3\)		$\mathrm{SU}(2)[C_{78}]$

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

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