Space of modular forms of level 54 and weight 6

• Label: 54.6
• Level: 54
• Weight: 6
• Dimension: 106
• Nonzero newspaces: 3
• Newform subspaces: 10
• Sturm bound: 972
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(972\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(54))\).

	Total	New	Old
Modular forms	435	106	329
Cusp forms	375	106	269
Eisenstein series	60	0	60

Trace form

106 * q + 4 * q^2 + 16 * q^4 + 282 * q^5 + 120 * q^6 - 172 * q^7 - 320 * q^8 - 660 * q^9 - 216 * q^10 + 846 * q^11 + 528 * q^12 + 3902 * q^13 + 944 * q^14 - 3258 * q^15 + 256 * q^16 - 7350 * q^17 + 5784 * q^18 - 646 * q^19 - 3840 * q^20 - 14592 * q^21 + 3552 * q^22 + 16218 * q^23 - 11045 * q^25 + 9536 * q^26 + 17631 * q^27 + 32 * q^28 + 20016 * q^29 - 10224 * q^30 + 17396 * q^31 + 1024 * q^32 - 73629 * q^33 + 2184 * q^34 - 28074 * q^35 + 15072 * q^36 + 4832 * q^37 + 70220 * q^38 + 24510 * q^39 - 3456 * q^40 + 24690 * q^41 - 30624 * q^42 - 28948 * q^43 - 24192 * q^44 - 138564 * q^45 - 35520 * q^46 - 140910 * q^47 - 1536 * q^48 - 35427 * q^49 + 42652 * q^50 + 166968 * q^51 + 62432 * q^52 + 440376 * q^53 + 119520 * q^54 + 143910 * q^55 + 15104 * q^56 - 39537 * q^57 - 99912 * q^58 - 296667 * q^59 - 52128 * q^60 - 10066 * q^61 - 198880 * q^62 - 336318 * q^63 - 118784 * q^64 - 59322 * q^65 + 60480 * q^66 - 89686 * q^67 + 32592 * q^68 - 21258 * q^69 - 69480 * q^70 + 141744 * q^71 - 109056 * q^72 + 92606 * q^73 + 144104 * q^74 + 153732 * q^75 + 57008 * q^76 + 356220 * q^77 + 107280 * q^78 + 448004 * q^79 + 21504 * q^80 + 275400 * q^81 - 34632 * q^82 + 100164 * q^83 + 86400 * q^84 + 396288 * q^85 + 417800 * q^86 - 185724 * q^87 - 79680 * q^88 - 467871 * q^89 - 274680 * q^90 - 234530 * q^91 - 110592 * q^92 - 797442 * q^93 - 539160 * q^94 - 1005114 * q^95 + 6144 * q^96 - 122272 * q^97 - 693828 * q^98 + 311652 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
54.6.a	\(\chi_{54}(1, \cdot)\)	54.6.a.a	1	1
		54.6.a.b	1
		54.6.a.c	1
		54.6.a.d	1
		54.6.a.e	1
		54.6.a.f	1
54.6.c	\(\chi_{54}(19, \cdot)\)	54.6.c.a	4	2
		54.6.c.b	6
54.6.e	\(\chi_{54}(7, \cdot)\)	54.6.e.a	42	6
		54.6.e.b	48

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(54)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)