Space of modular forms of level 513, weight 2, and Character 513.cd

• Label: 513.2.cd
• Level: $513$
• Weight: $2$
• Character orbit: 513.cd
• Rep. character: $\chi_{513}(116,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $108$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.cd (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(513, [\chi])\).

	Total	New	Old
Modular forms	396	132	264
Cusp forms	324	108	216
Eisenstein series	72	24	48

Trace form

108 * q + 9 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 - 12 * q^10 + 9 * q^11 - 6 * q^13 + 9 * q^14 + 9 * q^16 + 27 * q^17 - 15 * q^19 + 18 * q^20 - 6 * q^22 + 9 * q^23 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 18 * q^29 - 9 * q^31 - 27 * q^32 - 21 * q^34 + 45 * q^35 + 18 * q^38 - 30 * q^40 + 72 * q^41 - 27 * q^43 - 63 * q^44 - 18 * q^46 + 9 * q^47 + 30 * q^49 - 63 * q^50 + 15 * q^52 + 3 * q^55 + 63 * q^56 - 6 * q^58 - 99 * q^59 + 39 * q^61 + 18 * q^62 + 9 * q^65 + 27 * q^67 - 24 * q^70 - 45 * q^73 - 72 * q^74 - 3 * q^76 + 18 * q^77 - 6 * q^79 + 126 * q^80 - 3 * q^82 - 3 * q^85 + 9 * q^86 + 54 * q^89 - 9 * q^91 - 99 * q^92 + 9 * q^95 + 24 * q^97 - 27 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(513, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
513.2.cd.a	$513$	$2$	513.cd	171.ad	$18$	$108$	$18$	$4.096$		None			✓	✓	171.2.x.a	$2$	$0$	\(9\)	\(0\)	\(9\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(513, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(513, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)