Space of modular forms of level 54 and weight 3

• Label: 54.3
• Level: 54
• Weight: 3
• Dimension: 42
• Nonzero newspaces: 3
• Newform subspaces: 3
• Sturm bound: 486
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(486\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(54))\).

	Total	New	Old
Modular forms	192	42	150
Cusp forms	132	42	90
Eisenstein series	60	0	60

Trace form

42 * q + 36 * q^5 + 12 * q^6 + 12 * q^7 - 12 * q^9 - 24 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 72 * q^14 - 18 * q^15 - 48 * q^18 + 18 * q^19 - 36 * q^20 - 228 * q^21 + 48 * q^22 - 198 * q^23 - 72 * q^25 + 54 * q^27 - 12 * q^28 + 126 * q^29 + 144 * q^30 - 72 * q^31 + 324 * q^33 + 24 * q^34 + 486 * q^35 + 168 * q^36 + 78 * q^37 + 252 * q^38 + 102 * q^39 + 48 * q^40 + 36 * q^41 + 48 * q^42 + 72 * q^43 - 378 * q^45 - 48 * q^46 - 432 * q^47 - 24 * q^48 + 12 * q^49 - 54 * q^51 + 24 * q^52 - 36 * q^54 + 36 * q^55 - 144 * q^56 + 72 * q^57 - 24 * q^58 + 126 * q^59 + 36 * q^60 - 36 * q^61 + 318 * q^63 + 96 * q^64 - 72 * q^65 - 432 * q^66 - 738 * q^67 - 252 * q^68 - 522 * q^69 - 588 * q^70 - 648 * q^71 - 192 * q^72 - 276 * q^73 - 576 * q^74 - 438 * q^75 - 228 * q^76 - 252 * q^77 - 288 * q^78 + 96 * q^79 + 324 * q^81 + 192 * q^82 + 972 * q^83 + 216 * q^84 + 900 * q^85 + 648 * q^86 + 1062 * q^87 + 120 * q^88 + 648 * q^89 + 720 * q^90 + 204 * q^91 + 360 * q^92 + 462 * q^93 + 612 * q^94 + 72 * q^95 + 96 * q^96 + 618 * q^97 + 648 * q^98 + 126 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)

We only show spaces with odd 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
54.3.b	\(\chi_{54}(53, \cdot)\)	54.3.b.a	2	1
54.3.d	\(\chi_{54}(17, \cdot)\)	54.3.d.a	4	2
54.3.f	\(\chi_{54}(5, \cdot)\)	54.3.f.a	36	6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

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