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

• Label: 54.21.d
• Level: $54$
• Weight: $21$
• Character orbit: 54.d
• Rep. character: $\chi_{54}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $189$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(189\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	372	40	332
Cusp forms	348	40	308
Eisenstein series	24	0	24

Trace form

40 * q + 10485760 * q^4 - 29763918 * q^5 + 133479866 * q^7 + 35793208728 * q^11 + 39827158550 * q^13 - 187564400640 * q^14 - 5497558138880 * q^16 - 10560819523540 * q^19 - 15604865040384 * q^20 + 10829007458304 * q^22 + 95164852839678 * q^23 + 485893942617694 * q^25 + 139963783970816 * q^28 - 487337329131246 * q^29 - 386065992062842 * q^31 - 810410730184704 * q^34 + 7650497672534432 * q^37 + 27431157167935488 * q^38 + 76546903885431012 * q^41 - 10868849409851092 * q^43 + 13732137981788160 * q^46 - 220882065588142506 * q^47 - 201918836583922386 * q^49 - 84434006357065728 * q^50 - 20880901301862400 * q^52 - 689556443803109316 * q^55 - 98337764482744320 * q^56 + 289875600503808000 * q^58 + 4671324023815652220 * q^59 - 608513692992272866 * q^61 - 5764607523034234880 * q^64 - 4959300225343873626 * q^65 - 2581864509390888904 * q^67 + 5171455594224156672 * q^68 - 584784912675889152 * q^70 + 15022099327729072004 * q^73 - 7089371473773993984 * q^74 - 2768455473178869760 * q^76 + 30865724759591472834 * q^77 + 18532232803602736754 * q^79 - 35601230743051272192 * q^82 - 54829678294093455594 * q^83 + 43688870161052471388 * q^85 - 47393791396458614784 * q^86 - 5677518662299287552 * q^88 - 35182774173576758996 * q^91 + 49893790365609099264 * q^92 + 19892618446780047360 * q^94 - 332020921293200455200 * q^95 - 66463398176406835216 * 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.d.a	$54$	$21$	54.d	9.d	$6$	$40$	$20$	$136.897$		None			✓	✓	18.21.d.a	$2$	$0$	\(0\)	\(0\)	\(-29763918\)	\(133479866\)		$\mathrm{SU}(2)[C_{6}]$

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

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