Space of modular forms of level 54, weight 7, and Character 54.d

• Label: 54.7.d
• Level: $54$
• Weight: $7$
• Character orbit: 54.d
• Rep. character: $\chi_{54}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $63$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(63\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(54, [\chi])\).

	Total	New	Old
Modular forms	120	12	108
Cusp forms	96	12	84
Eisenstein series	24	0	24

Trace form

12 * q + 192 * q^4 - 432 * q^5 + 240 * q^7 - 378 * q^11 + 1680 * q^13 + 4752 * q^14 - 6144 * q^16 - 2820 * q^19 - 13824 * q^20 - 3600 * q^22 + 76248 * q^23 + 8094 * q^25 + 15360 * q^28 - 97092 * q^29 + 21480 * q^31 - 27360 * q^34 - 25536 * q^37 - 97632 * q^38 + 410562 * q^41 + 71430 * q^43 - 135072 * q^46 - 347652 * q^47 - 135954 * q^49 - 311040 * q^50 - 53760 * q^52 + 580392 * q^55 + 152064 * q^56 + 159264 * q^58 - 369738 * q^59 + 135744 * q^61 - 393216 * q^64 + 753840 * q^65 - 289938 * q^67 - 744768 * q^68 + 155952 * q^70 - 977700 * q^73 + 2197152 * q^74 - 45120 * q^76 + 159192 * q^77 - 764796 * q^79 + 1073088 * q^82 - 396900 * q^83 + 1619568 * q^85 - 3264624 * q^86 + 115200 * q^88 + 355584 * q^91 + 2439936 * q^92 - 736848 * q^94 + 2089260 * q^95 - 38874 * q^97

Decomposition of \(S_{7}^{\mathrm{new}}(54, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.7.d.a	$54$	$7$	54.d	9.d	$6$	$12$	$6$	$12.423$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None			✓	✓	18.7.d.a	$2$	$0$	\(0\)	\(0\)	\(-432\)	\(240\)	$2^{10}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}-2^{5}\beta _{2}q^{4}+(-48-24\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)