Space of modular forms of level 54, weight 9, and Character 54.b

• Label: 54.9.b
• Level: $54$
• Weight: $9$
• Character orbit: 54.b
• Rep. character: $\chi_{54}(53,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $81$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(81\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(54, [\chi])\).

	Total	New	Old
Modular forms	78	10	68
Cusp forms	66	10	56
Eisenstein series	12	0	12

Trace form

10 * q - 1280 * q^4 - 3658 * q^7 + 8448 * q^10 + 71090 * q^13 + 163840 * q^16 + 2306 * q^19 - 384000 * q^22 + 230182 * q^25 + 468224 * q^28 - 127144 * q^31 - 3884544 * q^34 + 6875498 * q^37 - 1081344 * q^40 - 23144764 * q^43 + 6300672 * q^46 + 14456352 * q^49 - 9099520 * q^52 + 63437004 * q^55 - 20659200 * q^58 + 11655626 * q^61 - 20971520 * q^64 - 15060070 * q^67 - 70411776 * q^70 - 10846114 * q^73 - 295168 * q^76 + 26971610 * q^79 + 26995200 * q^82 + 123210072 * q^85 + 49152000 * q^88 - 160865834 * q^91 - 290075136 * q^94 + 57846470 * q^97

Decomposition of \(S_{9}^{\mathrm{new}}(54, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.9.b.a	$54$	$9$	54.b	3.b	$2$	$2$	$2$	$21.998$	\(\Q(\sqrt{-2}) \)	None		✓			54.9.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4130\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2^{7}q^{4}+60\beta q^{5}-2065q^{7}+\cdots\)
54.9.b.b	$54$	$9$	54.b	3.b	$2$	$4$	$4$	$21.998$	\(\Q(\sqrt{-2}, \sqrt{79})\)	None		✓			54.9.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(164\)	$2^{9}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2^{7}q^{4}+(-21\beta _{1}+\beta _{2})q^{5}+\cdots\)
54.9.b.c	$54$	$9$	54.b	3.b	$2$	$4$	$4$	$21.998$	\(\Q(\zeta_{8})\)	None		✓			54.9.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(308\)	$2^{5}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta_{2} q^{2}-128 q^{4}+(51\beta_{2}-11\beta_1)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)