Space of modular forms of level 54, weight 8, and Character 54.e

• Label: 54.8.e
• Level: $54$
• Weight: $8$
• Character orbit: 54.e
• Rep. character: $\chi_{54}(7,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $126$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(54, [\chi])\).

	Total	New	Old
Modular forms	390	126	264
Cusp forms	366	126	240
Eisenstein series	24	0	24

Trace form

126 * q + 426 * q^5 - 1392 * q^6 + 1536 * q^8 + 3444 * q^9 - 18267 * q^11 - 2496 * q^12 + 26832 * q^14 - 12762 * q^15 + 58956 * q^17 + 72528 * q^18 - 54528 * q^20 + 124512 * q^21 - 105768 * q^22 + 284712 * q^23 + 215982 * q^25 - 632736 * q^26 - 575721 * q^27 + 264306 * q^29 + 903456 * q^30 - 595962 * q^31 - 420039 * q^33 + 266184 * q^34 - 642162 * q^35 - 683904 * q^36 + 399264 * q^38 - 2367906 * q^39 + 1053903 * q^41 + 841152 * q^42 + 1080963 * q^43 + 511104 * q^44 + 4105404 * q^45 + 4733640 * q^47 - 319488 * q^48 - 976014 * q^49 - 1347552 * q^50 - 2704752 * q^51 - 5903952 * q^53 - 191520 * q^54 + 1717248 * q^56 + 1748997 * q^57 + 4371630 * q^59 + 2418048 * q^60 - 3865446 * q^61 + 5719872 * q^62 + 8843682 * q^63 - 16515072 * q^64 - 4923066 * q^65 - 8709120 * q^66 - 14387841 * q^67 - 7527936 * q^68 - 1636398 * q^69 + 3492000 * q^70 + 7063224 * q^71 + 9719808 * q^72 - 7541874 * q^73 + 23032272 * q^74 + 42538332 * q^75 + 402048 * q^76 - 2583966 * q^77 - 17129952 * q^78 - 32831064 * q^79 - 6144000 * q^80 - 55973592 * q^81 - 7892640 * q^83 + 10575360 * q^84 + 15813000 * q^85 + 25345656 * q^86 + 68772492 * q^87 + 13538304 * q^88 + 54045951 * q^89 + 6277680 * q^90 - 6630138 * q^91 - 9441408 * q^92 - 38380038 * q^93 - 34755552 * q^94 - 57195498 * q^95 - 8454144 * q^96 - 42777531 * q^97 + 29047800 * q^98 + 140319180 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(54, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.8.e.a	$54$	$8$	54.e	27.e	$9$	$60$	$10$	$16.869$		None		✓			54.8.e.a	$2$	$0$	\(0\)	\(0\)	\(213\)	\(1677\)		$\mathrm{SU}(2)[C_{9}]$
54.8.e.b	$54$	$8$	54.e	27.e	$9$	$66$	$11$	$16.869$		None		✓	✓		54.8.e.b	$2$	$0$	\(0\)	\(0\)	\(213\)	\(-1677\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{8}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)