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

• Label: 513.2.bk
• Level: $513$
• Weight: $2$
• Character orbit: 513.bk
• Rep. character: $\chi_{513}(86,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $348$
• 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.bk (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 513 \)
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	372	372	0
Cusp forms	348	348	0
Eisenstein series	24	24	0

Trace form

348 * q - 6 * q^2 - 3 * q^3 - 6 * q^4 - 9 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9 + 15 * q^10 - 6 * q^12 - 6 * q^13 - 3 * q^14 + 45 * q^15 - 36 * q^17 - 6 * q^18 - 12 * q^19 + 9 * q^20 - 6 * q^21 - 36 * q^22 + 18 * q^23 + 21 * q^24 - 312 * q^25 - 18 * q^26 + 12 * q^28 + 15 * q^29 + 33 * q^30 - 9 * q^31 + 6 * q^32 + 3 * q^33 - 9 * q^34 + 21 * q^35 + 33 * q^36 - 45 * q^38 + 12 * q^39 + 36 * q^40 + 72 * q^41 + 63 * q^42 - 24 * q^43 - 39 * q^44 + 81 * q^45 - 27 * q^46 - 132 * q^48 - 3 * q^49 - 39 * q^50 - 30 * q^51 - 12 * q^52 + 12 * q^53 - 18 * q^54 + 18 * q^55 + 147 * q^56 - 99 * q^57 - 54 * q^59 + 96 * q^60 - 3 * q^61 + 21 * q^62 - 75 * q^63 - 147 * q^64 + 54 * q^65 - 3 * q^66 - 24 * q^67 - 42 * q^68 + 42 * q^69 + 54 * q^70 - 18 * q^71 - 33 * q^72 - 21 * q^73 + 27 * q^74 - 153 * q^75 - 6 * q^76 - 57 * q^77 + 81 * q^78 - 6 * q^79 + 129 * q^80 - 45 * q^81 - 9 * q^83 - 3 * q^84 + 9 * q^85 - 123 * q^86 + 66 * q^87 + 6 * q^88 + 9 * q^89 - 36 * q^90 - 24 * q^91 + 84 * q^92 - 69 * q^93 + 6 * q^94 - 36 * q^95 - 81 * q^96 + 48 * q^97 + 228 * q^98 - 129 * q^99

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.bk.a	$513$	$2$	513.bk	513.ak	$18$	$348$	$58$	$4.096$		None		✓	✓	✓	513.2.bi.a	$2$	$0$	\(-6\)	\(-3\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{18}]$