Space of modular forms of level 819, weight 2, and Character 819.dz

• Label: 819.2.dz
• Level: $819$
• Weight: $2$
• Character orbit: 819.dz
• Rep. character: $\chi_{819}(614,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dz (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 819 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).

	Total	New	Old
Modular forms	232	232	0
Cusp forms	216	216	0
Eisenstein series	16	16	0

Trace form

216 * q - 3 * q^2 - 3 * q^3 + 103 * q^4 - 12 * q^5 - q^7 - q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 + 3 * q^13 - 6 * q^14 - 18 * q^15 - 95 * q^16 + 14 * q^18 - 6 * q^19 - 12 * q^20 - 2 * q^21 - 20 * q^22 - 15 * q^23 + 30 * q^24 + 180 * q^25 - 30 * q^26 + 18 * q^27 + 20 * q^28 - 7 * q^30 + 6 * q^31 + 9 * q^32 - 3 * q^33 + 6 * q^34 - 3 * q^35 + 30 * q^36 - 2 * q^37 + 48 * q^38 + 3 * q^39 - 30 * q^42 - 2 * q^43 - 66 * q^44 - 20 * q^46 - 24 * q^47 + 12 * q^48 + 3 * q^49 - 33 * q^50 + 2 * q^51 + 36 * q^52 + 12 * q^53 - 6 * q^54 + 15 * q^55 + 6 * q^56 + 10 * q^57 + 7 * q^58 + 3 * q^59 - 41 * q^60 - 24 * q^62 - 23 * q^63 - 172 * q^64 - 39 * q^65 - 12 * q^67 - 3 * q^68 + 18 * q^69 - 45 * q^70 + 77 * q^72 - 12 * q^73 - 87 * q^74 - 39 * q^75 - 36 * q^76 - 42 * q^77 + 34 * q^78 - 3 * q^79 + 81 * q^80 + 19 * q^81 - 18 * q^82 + 6 * q^84 + 18 * q^85 + 42 * q^87 - 13 * q^88 - 30 * q^89 - 96 * q^90 + 18 * q^91 - 24 * q^92 + 10 * q^93 - 33 * q^95 + 42 * q^96 + 3 * q^97 - 29 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
819.2.dz.a	$819$	$2$	819.dz	819.cz	$6$	$216$	$108$	$6.540$		None		✓	✓	✓	819.2.bn.a	$2$	$0$	\(-3\)	\(-3\)	\(-12\)	\(-1\)		$\mathrm{SU}(2)[C_{6}]$