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

• Label: 19.4.c
• Level: $19$
• Weight: $4$
• Character orbit: 19.c
• Rep. character: $\chi_{19}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $6$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(6\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	12	12	0
Cusp forms	8	8	0
Eisenstein series	4	4	0

Trace form

8 * q - 3 * q^2 - 2 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 12 * q^7 + 18 * q^8 - 4 * q^9 - 32 * q^10 - 10 * q^11 + 42 * q^12 - 73 * q^13 - 142 * q^14 + 91 * q^15 - 43 * q^16 + 187 * q^17 + 60 * q^18 - 139 * q^19 + 668 * q^20 - 130 * q^21 - 121 * q^22 - 115 * q^23 - 39 * q^24 + 75 * q^25 - 320 * q^26 - 212 * q^27 - 454 * q^28 - 137 * q^29 - 128 * q^30 + 576 * q^31 - 465 * q^32 - 737 * q^33 + 916 * q^34 - 324 * q^35 + 938 * q^36 + 1260 * q^37 - 498 * q^38 + 1962 * q^39 - 690 * q^40 - 278 * q^41 - 266 * q^42 + 43 * q^43 + 433 * q^44 - 1772 * q^45 - 1012 * q^46 - 537 * q^47 + 39 * q^48 - 760 * q^49 + 1270 * q^50 - 805 * q^51 - 1074 * q^52 + 623 * q^53 + 53 * q^54 + 1170 * q^55 + 2076 * q^56 - 717 * q^57 + 3352 * q^58 - 316 * q^59 - 1006 * q^60 - 1077 * q^61 - 496 * q^62 + 912 * q^63 - 2602 * q^64 + 186 * q^65 - 863 * q^66 + 184 * q^67 - 1540 * q^68 + 1542 * q^69 - 1908 * q^70 - 1995 * q^71 + 1854 * q^72 - 116 * q^73 + 908 * q^74 + 3014 * q^75 + 1583 * q^76 + 1364 * q^77 - 748 * q^78 + 483 * q^79 + 470 * q^80 + 104 * q^81 - 143 * q^82 - 890 * q^83 - 828 * q^84 + 1575 * q^85 + 654 * q^86 - 1710 * q^87 - 1470 * q^88 - 713 * q^89 + 1588 * q^90 - 1356 * q^91 + 1408 * q^92 - 792 * q^93 - 2184 * q^94 - 2143 * q^95 + 286 * q^96 + 870 * q^97 - 2491 * q^98 - 1642 * 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.c.a	$19$	$4$	19.c	19.c	$3$	$4$	$2$	$1.121$	\(\Q(\sqrt{-3}, \sqrt{55})\)	None		✓			19.4.c.a	$2$	$0$	\(-2\)	\(0\)	\(14\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(7+7\beta _{2})q^{4}+\cdots\)
19.4.c.b	$19$	$4$	19.c	19.c	$3$	$4$	$2$	$1.121$	\(\Q(\sqrt{-3}, \sqrt{73})\)	None		✓			19.4.c.b	$2$	$0$	\(-1\)	\(-2\)	\(-19\)	\(40\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-11+\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots\)