Space of modular forms of level 19, weight 6, and Character 19.c

• Label: 19.6.c
• Level: $19$
• Weight: $6$
• Character orbit: 19.c
• Rep. character: $\chi_{19}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(19, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	16	16	0
Eisenstein series	4	4	0

Trace form

16 * q + 3 * q^2 + 28 * q^3 - 155 * q^4 + 10 * q^5 + 149 * q^6 + 208 * q^7 - 78 * q^8 - 616 * q^9 + 580 * q^10 + 632 * q^11 - 2238 * q^12 + 786 * q^13 + 2054 * q^14 + 796 * q^15 - 3779 * q^16 - 746 * q^17 + 8868 * q^18 - 5972 * q^19 - 7780 * q^20 - 292 * q^21 + 1841 * q^22 + 2084 * q^23 + 17913 * q^24 - 1378 * q^25 - 824 * q^26 - 28184 * q^27 - 9270 * q^28 + 5266 * q^29 + 41656 * q^30 - 15536 * q^31 + 21711 * q^32 + 14926 * q^33 - 2240 * q^34 - 7488 * q^35 - 41734 * q^36 - 3752 * q^37 - 33546 * q^38 - 36648 * q^39 + 9822 * q^40 + 21676 * q^41 + 8698 * q^42 + 9584 * q^43 - 43859 * q^44 + 69352 * q^45 + 90956 * q^46 + 29340 * q^47 - 1281 * q^48 + 16784 * q^49 - 98366 * q^50 + 23576 * q^51 + 71182 * q^52 - 30310 * q^53 + 49919 * q^54 - 36000 * q^55 - 305652 * q^56 + 107502 * q^57 - 286928 * q^58 + 101924 * q^59 + 19034 * q^60 + 36394 * q^61 - 69544 * q^62 - 44112 * q^63 + 459910 * q^64 + 106020 * q^65 + 219667 * q^66 - 50716 * q^67 + 27116 * q^68 - 110748 * q^69 + 159588 * q^70 + 116292 * q^71 - 468618 * q^72 + 36584 * q^73 - 278908 * q^74 - 518536 * q^75 + 311611 * q^76 - 446968 * q^77 + 136808 * q^78 + 110692 * q^79 + 253310 * q^80 - 99760 * q^81 - 92057 * q^82 + 229240 * q^83 + 452292 * q^84 + 113898 * q^85 - 126186 * q^86 + 342264 * q^87 - 347742 * q^88 + 356518 * q^89 + 741244 * q^90 - 337648 * q^91 + 52840 * q^92 - 368832 * q^93 - 781920 * q^94 + 265028 * q^95 - 1983074 * q^96 + 150004 * q^97 + 536843 * q^98 + 163952 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(19, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.6.c.a	$19$	$6$	19.c	19.c	$3$	$16$	$8$	$3.047$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	19.6.c.a	$2$	$0$	\(3\)	\(28\)	\(10\)	\(208\)	$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{3})q^{2}+(3+3\beta _{2}+\beta _{5})q^{3}+\cdots\)