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

• Label: 507.2.q
• Level: $507$
• Weight: $2$
• Character orbit: 507.q
• Rep. character: $\chi_{507}(16,\cdot)$
• Character field: $\Q(\zeta_{39})$
• Dimension: $744$
• 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.q (of order \(39\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{39})\)
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	744	768
Cusp forms	1416	744	672
Eisenstein series	96	0	96

Trace form

744 * q + 2 * q^2 + q^3 + 32 * q^4 + 8 * q^5 - q^7 - 12 * q^8 + 31 * q^9 + 2 * q^10 - 6 * q^11 - 4 * q^12 - 34 * q^13 + 24 * q^14 - 2 * q^15 + 26 * q^16 - 10 * q^17 - 4 * q^18 + 2 * q^20 + 10 * q^21 - 64 * q^22 - 6 * q^23 + 12 * q^24 - 46 * q^25 - 30 * q^26 - 2 * q^27 - 18 * q^28 - 8 * q^29 + 4 * q^30 - 62 * q^31 - 116 * q^32 - 2 * q^33 - 134 * q^34 - 10 * q^35 + 32 * q^36 + 12 * q^37 - 82 * q^38 + 6 * q^39 - 50 * q^40 + 10 * q^41 + 248 * q^42 - q^43 + 16 * q^44 - 4 * q^45 - 4 * q^46 - 12 * q^47 - 4 * q^48 - 140 * q^49 - 28 * q^50 - 8 * q^51 - 100 * q^52 - 128 * q^53 - 134 * q^55 - 40 * q^56 - 24 * q^57 - 78 * q^58 + 402 * q^59 - 104 * q^60 + q^61 - 150 * q^62 - q^63 - 44 * q^64 - 4 * q^65 - 96 * q^66 - 153 * q^67 - 136 * q^68 + 6 * q^69 - 200 * q^70 + 190 * q^71 + 6 * q^72 + 2 * q^73 - 196 * q^74 - q^75 + 56 * q^76 + 28 * q^77 - 102 * q^78 + 2 * q^79 + 22 * q^80 + 31 * q^81 - 132 * q^82 + 48 * q^83 - 14 * q^84 - 142 * q^85 - 156 * q^86 - 106 * q^87 + 484 * q^88 + 4 * q^89 - 4 * q^90 - 135 * q^91 + 24 * q^92 - 3 * q^93 - 170 * q^94 + 168 * q^95 - 8 * q^96 - 171 * q^97 + 22 * 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.q.a	$507$	$2$	507.q	169.i	$39$	$360$	$15$	$4.048$		None		✓			507.2.q.a	$2$	$0$	\(1\)	\(-15\)	\(2\)	\(2\)		$\mathrm{SU}(2)[C_{39}]$
507.2.q.b	$507$	$2$	507.q	169.i	$39$	$384$	$16$	$4.048$		None		✓	✓		507.2.q.b	$2$	$0$	\(1\)	\(16\)	\(6\)	\(-3\)		$\mathrm{SU}(2)[C_{39}]$

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

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