Space of modular forms of level 19, weight 2, and Character 19.e

• Label: 19.2.e
• Level: $19$
• Weight: $2$
• Character orbit: 19.e
• Rep. character: $\chi_{19}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	19.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(19, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	6	6	0
Eisenstein series	12	12	0

Trace form

6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9 + 9 * q^10 + 3 * q^12 - 3 * q^13 - 3 * q^14 + 3 * q^15 - 18 * q^16 + 3 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 + 6 * q^23 + 15 * q^24 + 15 * q^26 + 6 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 9 * q^33 + 6 * q^35 - 24 * q^36 - 15 * q^38 - 24 * q^39 + 21 * q^41 - 3 * q^42 - 3 * q^43 + 9 * q^44 - 15 * q^45 - 18 * q^46 - 3 * q^47 - 3 * q^48 + 15 * q^49 - 15 * q^50 + 3 * q^51 + 15 * q^52 - 3 * q^53 + 30 * q^54 + 18 * q^55 - 6 * q^56 + 24 * q^57 + 36 * q^58 + 12 * q^59 - 6 * q^60 - 12 * q^61 - 12 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^65 - 9 * q^66 - 30 * q^67 - 15 * q^68 - 12 * q^69 - 9 * q^70 - 6 * q^71 - 12 * q^72 - 12 * q^73 + 15 * q^74 + 30 * q^75 + 36 * q^76 - 18 * q^77 + 15 * q^78 - 39 * q^79 + 3 * q^80 + 6 * q^81 - 54 * q^82 + 3 * q^84 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 12 * q^89 + 18 * q^90 + 15 * q^91 + 42 * q^92 + 9 * q^93 + 18 * q^94 + 39 * q^95 + 18 * q^96 + 18 * q^97 - 9 * q^98 + 9 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(19, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.2.e.a	$19$	$2$	19.e	19.e	$9$	$6$	$1$	$0.152$	\(\Q(\zeta_{18})\)	None		✓	✓	✓	19.2.e.a	$2$	$0$	\(-6\)	\(-3\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)