Space of modular forms of level 19, weight 9, and Character 19.b

• Label: 19.9.b
• Level: $19$
• Weight: $9$
• Character orbit: 19.b
• Rep. character: $\chi_{19}(18,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $2$
• Sturm bound: $15$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	19.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(15\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(19, [\chi])\).

	Total	New	Old
Modular forms	15	15	0
Cusp forms	13	13	0
Eisenstein series	2	2	0

Trace form

13 * q - 1318 * q^4 - 281 * q^5 + 986 * q^6 + 4213 * q^7 - 34145 * q^9 + 16039 * q^11 + 34650 * q^16 - 206423 * q^17 - 166985 * q^19 + 212500 * q^20 + 817384 * q^23 - 1485226 * q^24 + 790240 * q^25 + 2423070 * q^26 - 2272858 * q^28 + 1776176 * q^30 - 3675919 * q^35 + 1642908 * q^36 - 3002394 * q^38 - 1968898 * q^39 + 10898030 * q^42 - 8285397 * q^43 - 23114120 * q^44 - 2715137 * q^45 + 19237279 * q^47 + 34441398 * q^49 - 25237238 * q^54 + 26228137 * q^55 - 8487050 * q^57 - 32278162 * q^58 + 29957055 * q^61 - 3995844 * q^62 - 93509813 * q^63 + 44055462 * q^64 + 91456852 * q^66 + 35613718 * q^68 - 61077851 * q^73 - 168372588 * q^74 - 75731912 * q^76 + 111441401 * q^77 + 172214656 * q^80 - 76849159 * q^81 - 17376524 * q^82 + 145036438 * q^83 - 249876075 * q^85 + 27034246 * q^87 - 156586838 * q^92 - 10067084 * q^93 + 213792643 * q^95 + 263607090 * q^96 - 223903117 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(19, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
19.9.b.a	$19$	$9$	19.b	19.b	$2$	$1$	$1$	$7.740$	\(\Q\)	\(\Q(\sqrt{-19}) \)	✓	✓			19.9.b.a	$2$	$0$	\(0\)	\(0\)	\(-289\)	\(527\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{8}q^{4}-17^{2}q^{5}+527q^{7}+3^{8}q^{9}+\cdots\)
19.9.b.b	$19$	$9$	19.b	19.b	$2$	$12$	$12$	$7.740$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		19.9.b.b	$2$	$0$	\(0\)	\(0\)	\(8\)	\(3686\)	$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-131+\beta _{2})q^{4}+\cdots\)