Space of modular forms of level 54 and weight 8

• Label: 54.8
• Level: 54
• Weight: 8
• Dimension: 150
• Nonzero newspaces: 3
• Newform subspaces: 12
• Sturm bound: 1296
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1296\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(54))\).

	Total	New	Old
Modular forms	597	150	447
Cusp forms	537	150	387
Eisenstein series	60	0	60

Trace form

150 * q - 8 * q^2 + 192 * q^4 + 318 * q^5 - 1392 * q^6 + 1452 * q^7 + 2560 * q^8 + 3444 * q^9 - 5520 * q^10 - 27018 * q^11 - 2496 * q^12 + 3330 * q^13 + 24800 * q^14 - 12762 * q^15 + 12288 * q^16 + 140718 * q^17 + 72528 * q^18 + 7818 * q^19 - 61440 * q^20 + 124512 * q^21 - 99840 * q^22 + 326394 * q^23 + 460569 * q^25 - 368896 * q^26 - 575721 * q^27 + 61056 * q^28 - 258624 * q^29 + 903456 * q^30 - 628932 * q^31 - 32768 * q^32 - 420039 * q^33 + 615216 * q^34 + 1938606 * q^35 - 683904 * q^36 - 111528 * q^37 - 513544 * q^38 - 2367906 * q^39 - 353280 * q^40 - 643794 * q^41 + 841152 * q^42 + 3173316 * q^43 + 1631232 * q^44 + 4105404 * q^45 + 436224 * q^46 + 3746298 * q^47 - 319488 * q^48 - 6019689 * q^49 - 2671736 * q^50 - 2704752 * q^51 + 213120 * q^52 - 5970504 * q^53 - 191520 * q^54 - 2786706 * q^55 + 1587200 * q^56 + 1748997 * q^57 - 2566704 * q^58 + 1485981 * q^59 + 2418048 * q^60 + 2751954 * q^61 + 8064128 * q^62 + 8843682 * q^63 - 10223616 * q^64 - 2809830 * q^65 - 8709120 * q^66 - 20343990 * q^67 - 10144320 * q^68 - 1636398 * q^69 - 5456112 * q^70 - 4176528 * q^71 + 9719808 * q^72 - 596310 * q^73 + 18383984 * q^74 + 42538332 * q^75 + 5393088 * q^76 + 9518292 * q^77 - 17129952 * q^78 - 59249124 * q^79 - 5259264 * q^80 - 55973592 * q^81 - 1495920 * q^82 + 14541996 * q^83 + 10575360 * q^84 + 48420144 * q^85 + 27070352 * q^86 + 68772492 * q^87 + 13917696 * q^88 + 4179531 * q^89 + 6277680 * q^90 + 3912486 * q^91 - 6773760 * q^92 - 38380038 * q^93 - 35265168 * q^94 - 8836122 * q^95 - 8454144 * q^96 - 60018120 * q^97 + 57131208 * q^98 + 140319180 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(54))\)

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
54.8.a	\(\chi_{54}(1, \cdot)\)	54.8.a.a	1	1
		54.8.a.b	1
		54.8.a.c	1
		54.8.a.d	1
		54.8.a.e	1
		54.8.a.f	1
		54.8.a.g	2
		54.8.a.h	2
54.8.c	\(\chi_{54}(19, \cdot)\)	54.8.c.a	6	2
		54.8.c.b	8
54.8.e	\(\chi_{54}(7, \cdot)\)	54.8.e.a	60	6
		54.8.e.b	66

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

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