Space of modular forms of level 54 and weight 4

• Label: 54.4
• Level: 54
• Weight: 4
• Dimension: 64
• Nonzero newspaces: 3
• Newform subspaces: 8
• Sturm bound: 648
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(648\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(54))\).

	Total	New	Old
Modular forms	273	64	209
Cusp forms	213	64	149
Eisenstein series	60	0	60

Trace form

64 * q - 2 * q^2 + 4 * q^4 - 42 * q^5 + 12 * q^6 + 56 * q^7 + 40 * q^8 + 96 * q^9 + 60 * q^10 - 90 * q^11 - 12 * q^12 - 142 * q^13 - 232 * q^14 - 72 * q^15 + 16 * q^16 + 282 * q^17 + 276 * q^18 + 20 * q^19 + 120 * q^20 + 204 * q^21 + 48 * q^22 - 396 * q^23 + 19 * q^25 - 544 * q^26 - 1377 * q^27 + 80 * q^28 - 414 * q^29 - 504 * q^30 + 236 * q^31 - 32 * q^32 + 135 * q^33 - 900 * q^34 - 84 * q^35 + 600 * q^36 - 142 * q^37 + 350 * q^38 + 696 * q^39 + 240 * q^40 + 2226 * q^41 + 912 * q^42 + 1028 * q^43 + 576 * q^44 + 1674 * q^45 + 672 * q^46 + 822 * q^47 + 192 * q^48 + 417 * q^49 - 1406 * q^50 - 3186 * q^51 - 568 * q^52 - 4116 * q^53 - 1008 * q^54 - 306 * q^55 - 928 * q^56 - 3141 * q^57 - 204 * q^58 - 135 * q^59 + 1008 * q^60 + 1082 * q^61 + 3152 * q^62 + 3936 * q^63 - 1088 * q^64 + 8970 * q^65 + 4320 * q^66 + 3908 * q^67 + 876 * q^68 + 6120 * q^69 + 1308 * q^70 + 552 * q^71 - 192 * q^72 - 3166 * q^73 - 3940 * q^74 - 7998 * q^75 - 2260 * q^76 - 11016 * q^77 - 5688 * q^78 - 8476 * q^79 - 384 * q^80 - 6156 * q^81 - 2172 * q^82 - 4560 * q^83 - 2160 * q^84 - 7236 * q^85 - 3532 * q^86 - 2178 * q^87 - 456 * q^88 + 6753 * q^89 + 1260 * q^90 + 4234 * q^91 + 3312 * q^92 + 9696 * q^93 + 6996 * q^94 + 15918 * q^95 + 960 * q^96 + 9506 * q^97 + 2754 * q^98 + 6282 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)

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
54.4.a	\(\chi_{54}(1, \cdot)\)	54.4.a.a	1	1
		54.4.a.b	1
		54.4.a.c	1
		54.4.a.d	1
54.4.c	\(\chi_{54}(19, \cdot)\)	54.4.c.a	2	2
		54.4.c.b	4
54.4.e	\(\chi_{54}(7, \cdot)\)	54.4.e.a	24	6
		54.4.e.b	30

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

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