Space of modular forms of level 189, weight 3, and Character 189.j

• Label: 189.3.j
• Level: $189$
• Weight: $3$
• Character orbit: 189.j
• Rep. character: $\chi_{189}(44,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(189, [\chi])\).

	Total	New	Old
Modular forms	108	36	72
Cusp forms	84	28	56
Eisenstein series	24	8	16

Trace form

28 * q - 50 * q^4 + 3 * q^5 - 2 * q^7 + 6 * q^10 - 15 * q^11 - 7 * q^13 + 84 * q^14 + 70 * q^16 - 27 * q^17 - 16 * q^19 - 6 * q^20 + 6 * q^22 - 96 * q^23 + 31 * q^25 - 84 * q^26 - 8 * q^28 + 114 * q^29 - 34 * q^31 - 6 * q^34 + 30 * q^35 - 13 * q^37 + 69 * q^38 - 48 * q^40 + 78 * q^41 - 34 * q^43 + 327 * q^44 + 18 * q^46 + 10 * q^49 - 357 * q^50 + 17 * q^52 - 108 * q^53 + 66 * q^55 - 552 * q^56 + 33 * q^58 - 112 * q^61 - 32 * q^64 + 68 * q^67 + 540 * q^68 - 21 * q^70 - 100 * q^73 + 69 * q^74 + 134 * q^76 + 426 * q^77 - 100 * q^79 + 3 * q^80 - 6 * q^82 - 354 * q^83 - 57 * q^85 - 753 * q^86 - 87 * q^88 - 477 * q^89 + 107 * q^91 + 1092 * q^92 + 366 * q^94 + 17 * q^97 + 123 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(189, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
189.3.j.a	$189$	$3$	189.j	63.j	$6$	$6$	$3$	$5.150$	6.0.63369648.1	None					63.3.j.a	$2$	$0$	\(0\)	\(0\)	\(15\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{4}-\beta _{5})q^{2}+(-4-\beta _{1})q^{4}+\cdots\)
189.3.j.b	$189$	$3$	189.j	63.j	$6$	$22$	$11$	$5.150$		None			✓		63.3.j.b	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(189, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)