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

• Label: 9.19.b
• Level: $9$
• Weight: $19$
• Character orbit: 9.b
• Rep. character: $\chi_{9}(8,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $19$
• Trace bound: $0$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	20	6	14
Cusp forms	16	6	10
Eisenstein series	4	0	4

Trace form

6 * q - 252228 * q^4 + 19180488 * q^7 - 1977017220 * q^10 - 9548549232 * q^13 - 207185871864 * q^16 - 656204938080 * q^19 - 7584065488368 * q^22 - 21243296221590 * q^25 - 29705497415664 * q^28 - 98608210584 * q^31 + 260913445492212 * q^34 + 419020081378356 * q^37 + 648389714590440 * q^40 + 370083581009616 * q^43 - 1216221762695184 * q^46 - 5618413418872518 * q^49 - 7021328175776544 * q^52 - 11859820956568080 * q^55 - 4823292380886396 * q^58 + 53682979243926828 * q^61 + 44907118634214384 * q^64 + 104029134116976624 * q^67 - 44449372539736560 * q^70 + 71435015065643808 * q^73 - 427178828391967680 * q^76 - 191467262028180264 * q^79 - 840489249928382676 * q^82 + 869913666590118300 * q^85 - 517893138356089248 * q^88 + 1675089167400159936 * q^91 - 353355842669446224 * q^94 + 3551812318571376864 * q^97

Decomposition of \(S_{19}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.19.b.a	$9$	$19$	9.b	3.b	$2$	$6$	$6$	$18.485$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓	✓	✓	9.19.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(19180488\)	$2^{7}\cdot 3^{33}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-42038-\beta _{2})q^{4}+(1082\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{19}^{\mathrm{old}}(9, [\chi])\) into lower level spaces

\( S_{19}^{\mathrm{old}}(9, [\chi]) \simeq \) \(S_{19}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)