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

• Label: 507.2.m
• Level: $507$
• Weight: $2$
• Character orbit: 507.m
• Rep. character: $\chi_{507}(40,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $384$
• 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.m (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{13})\)
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	384	360
Cusp forms	696	384	312
Eisenstein series	48	0	48

Trace form

384 * q - 2 * q^2 - 2 * q^3 - 36 * q^4 - 8 * q^5 - 4 * q^7 - 6 * q^8 - 32 * q^9 - 8 * q^10 - 12 * q^11 - 6 * q^12 + 40 * q^13 - 24 * q^14 - 4 * q^15 - 60 * q^16 - 20 * q^17 - 2 * q^18 - 20 * q^19 - 56 * q^20 - 12 * q^21 + 16 * q^22 - 12 * q^23 - 12 * q^24 - 60 * q^25 - 42 * q^26 - 2 * q^27 - 44 * q^28 - 16 * q^29 - 4 * q^30 + 24 * q^31 + 56 * q^32 - 4 * q^33 + 62 * q^34 - 20 * q^35 - 36 * q^36 - 32 * q^37 + 82 * q^38 - 10 * q^39 + 14 * q^40 - 64 * q^41 + 94 * q^42 - 28 * q^43 - 76 * q^44 - 8 * q^45 - 80 * q^46 - 36 * q^47 - 30 * q^48 + 68 * q^49 - 86 * q^50 - 16 * q^51 + 42 * q^52 + 116 * q^53 + 62 * q^55 - 128 * q^56 - 20 * q^57 - 24 * q^58 + 132 * q^59 + 44 * q^60 - 48 * q^61 + 30 * q^62 - 4 * q^63 - 128 * q^64 - 80 * q^65 + 72 * q^66 + 88 * q^67 + 58 * q^68 - 12 * q^69 + 56 * q^70 + 2 * q^71 - 6 * q^72 - 88 * q^73 + 94 * q^74 - 30 * q^75 + 104 * q^76 - 64 * q^77 + 90 * q^78 - 76 * q^79 - 184 * q^80 - 32 * q^81 + 42 * q^82 - 84 * q^83 - 36 * q^84 + 76 * q^85 + 60 * q^86 + 64 * q^87 + 104 * q^88 - 112 * q^89 - 8 * q^90 + 4 * q^91 - 132 * q^92 + 110 * q^93 + 2 * q^94 - 12 * q^95 - 64 * q^96 + 52 * q^97 - 178 * q^98 - 12 * q^99

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.m.a	$507$	$2$	507.m	169.g	$13$	$180$	$15$	$4.048$		None		✓			507.2.m.a	$2$	$0$	\(-1\)	\(15\)	\(-2\)	\(4\)		$\mathrm{SU}(2)[C_{13}]$
507.2.m.b	$507$	$2$	507.m	169.g	$13$	$204$	$17$	$4.048$		None		✓	✓		507.2.m.b	$2$	$0$	\(-1\)	\(-17\)	\(-6\)	\(-8\)		$\mathrm{SU}(2)[C_{13}]$

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

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