Space of modular forms of level 54 and weight 9

• Label: 54.9
• Level: 54
• Weight: 9
• Dimension: 170
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 1458
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1458\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(54))\).

	Total	New	Old
Modular forms	678	170	508
Cusp forms	618	170	448
Eisenstein series	60	0	60

Trace form

170 * q - 256 * q^4 + 1764 * q^5 + 768 * q^6 - 5504 * q^7 + 25908 * q^9 + 8448 * q^10 - 91512 * q^11 - 21504 * q^12 + 67720 * q^13 + 188928 * q^14 - 70002 * q^15 + 32768 * q^16 - 182784 * q^18 + 364486 * q^19 - 112896 * q^20 - 2071668 * q^21 - 260352 * q^22 - 758142 * q^23 + 178394 * q^25 - 4137588 * q^27 - 4352 * q^28 - 4842 * q^29 - 861696 * q^30 - 1426196 * q^31 + 10547334 * q^33 - 4325376 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 10218826 * q^37 + 15378048 * q^38 + 4239102 * q^39 - 1081344 * q^40 - 24892128 * q^41 - 11028480 * q^42 - 27217772 * q^43 - 12558942 * q^45 + 13718016 * q^46 + 50154444 * q^47 + 3440640 * q^48 + 744210 * q^49 - 55489536 * q^50 - 3281850 * q^51 - 8668160 * q^52 + 16379136 * q^54 + 58852728 * q^55 + 24182784 * q^56 - 13553658 * q^57 - 28512000 * q^58 - 180471384 * q^59 - 26125056 * q^60 - 23245784 * q^61 + 108329070 * q^63 + 96468992 * q^64 + 148758480 * q^65 + 152091648 * q^66 + 181987522 * q^67 + 18888192 * q^68 - 40190130 * q^69 - 222851328 * q^70 - 251437608 * q^71 - 60948480 * q^72 - 3128600 * q^73 + 6778368 * q^74 + 138868662 * q^75 + 90880000 * q^76 + 555602292 * q^77 + 201203712 * q^78 + 198320380 * q^79 - 23838948 * q^81 - 110350848 * q^82 - 597057804 * q^83 - 128300544 * q^84 - 345701700 * q^85 + 125141760 * q^86 + 34353810 * q^87 + 104546304 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 47381116 * q^91 - 70783488 * q^92 + 285095622 * q^93 - 372903168 * q^94 - 823047192 * q^95 - 88080384 * q^96 - 516486314 * q^97 - 234233856 * q^98 + 26756370 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(54))\)

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
54.9.b	\(\chi_{54}(53, \cdot)\)	54.9.b.a	2	1
		54.9.b.b	4
		54.9.b.c	4
54.9.d	\(\chi_{54}(17, \cdot)\)	54.9.d.a	16	2
54.9.f	\(\chi_{54}(5, \cdot)\)	54.9.f.a	144	6

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

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