Space of modular forms of level 19, weight 4, and Character 19.e

• Label: 19.4.e
• Level: $19$
• Weight: $4$
• Character orbit: 19.e
• Rep. character: $\chi_{19}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(19, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	24	24	0
Eisenstein series	12	12	0

Trace form

24 * q - 6 * q^2 - 3 * q^3 - 24 * q^4 - 6 * q^5 + 42 * q^6 + 3 * q^7 - 75 * q^8 - 51 * q^9 + 75 * q^10 + 39 * q^11 - 219 * q^12 - 156 * q^13 + 93 * q^14 - 192 * q^15 + 504 * q^16 + 12 * q^17 + 264 * q^18 + 546 * q^19 - 198 * q^20 + 453 * q^21 - 6 * q^22 + 6 * q^23 + 192 * q^24 - 498 * q^25 - 639 * q^26 - 870 * q^27 - 1368 * q^28 - 630 * q^29 - 522 * q^30 - 591 * q^31 + 147 * q^32 + 1506 * q^33 - 408 * q^34 + 2001 * q^35 + 1059 * q^36 - 72 * q^37 + 2934 * q^38 + 336 * q^39 + 2886 * q^40 - 477 * q^41 + 237 * q^42 + 588 * q^43 - 3423 * q^44 - 1569 * q^45 - 1728 * q^46 - 1242 * q^47 - 4599 * q^48 - 639 * q^49 - 1788 * q^50 + 9 * q^51 + 2733 * q^52 - 300 * q^53 + 3777 * q^54 + 315 * q^55 + 4638 * q^56 + 3342 * q^57 - 2820 * q^58 + 2097 * q^59 + 1116 * q^60 - 2316 * q^61 - 1320 * q^62 - 2979 * q^63 - 1785 * q^64 - 2433 * q^65 - 1590 * q^66 + 57 * q^67 - 438 * q^68 - 1767 * q^69 - 213 * q^70 - 792 * q^71 - 1686 * q^72 + 4068 * q^73 + 4287 * q^74 + 1332 * q^75 + 5538 * q^76 + 3786 * q^77 + 2121 * q^78 + 1824 * q^79 - 2739 * q^80 + 1536 * q^81 + 2205 * q^82 + 1071 * q^83 - 1437 * q^84 - 2394 * q^85 - 5256 * q^86 + 759 * q^87 + 1101 * q^88 - 3006 * q^89 - 3822 * q^90 - 3285 * q^91 - 1452 * q^92 - 135 * q^93 - 1086 * q^94 - 3078 * q^95 - 1590 * q^96 - 2535 * q^97 - 2403 * q^98 + 492 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(19, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.4.e.a	$19$	$4$	19.e	19.e	$9$	$24$	$4$	$1.121$		None		✓	✓	✓	19.4.e.a	$2$	$0$	\(-6\)	\(-3\)	\(-6\)	\(3\)		$\mathrm{SU}(2)[C_{9}]$