Space of modular forms of level 54, weight 21, and Character 54.b

• Label: 54.21.b
• Level: $54$
• Weight: $21$
• Character orbit: 54.b
• Rep. character: $\chi_{54}(53,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $3$
• Sturm bound: $189$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
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:			\(189\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(54, [\chi])\).

	Total	New	Old
Modular forms	186	26	160
Cusp forms	174	26	148
Eisenstein series	12	0	12

Trace form

26 * q - 13631488 * q^4 + 100727518 * q^7 + 11410710528 * q^10 + 547231356730 * q^13 + 7146825580544 * q^16 + 12086489555314 * q^19 - 473825280000 * q^22 - 366869649935698 * q^25 - 52810228957184 * q^28 + 672588288988768 * q^31 - 3983735200923648 * q^34 - 8072332126021118 * q^37 - 5982498601304064 * q^40 - 155583874953432716 * q^43 - 37486486052929536 * q^46 + 906048430794703680 * q^49 - 286906833557258240 * q^52 + 1123779595424330484 * q^55 + 107273858259517440 * q^58 - 1251721826983411934 * q^61 - 3746994889972252672 * q^64 + 1502248151172370330 * q^67 - 9064072265418817536 * q^70 + 27501013394782772254 * q^73 - 6336801435976466432 * q^76 + 11859936467954325178 * q^79 + 3384555120454287360 * q^82 + 42022433319928555752 * q^85 + 248420908400640000 * q^88 + 108408739581418563158 * q^91 + 84832525715310919680 * q^94 - 59596439607768595370 * q^97

Decomposition of \(S_{21}^{\mathrm{new}}(54, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.21.b.a	$54$	$21$	54.b	3.b	$2$	$6$	$6$	$136.897$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓			54.21.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-218826006\)	$2^{31}\cdot 3^{18}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2^{19}q^{4}+(776\beta _{1}-\beta _{4})q^{5}+\cdots\)
54.21.b.b	$54$	$21$	54.b	3.b	$2$	$8$	$8$	$136.897$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			54.21.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-36302648\)	$2^{51}\cdot 3^{36}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2^{19}q^{4}+(-4581\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
54.21.b.c	$54$	$21$	54.b	3.b	$2$	$12$	$12$	$136.897$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		54.21.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(355856172\)	$2^{63}\cdot 3^{90}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}-2^{19}q^{4}+(852\beta _{6}+\beta _{8})q^{5}+\cdots\)

Decomposition of \(S_{21}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{21}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{21}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)