Space of modular forms of level 54 and weight 2

• Label: 54.2
• Level: 54
• Weight: 2
• Dimension: 22
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 324
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(324\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(54))\).

	Total	New	Old
Modular forms	111	22	89
Cusp forms	52	22	30
Eisenstein series	59	0	59

Trace form

22 * q + q^2 + q^4 - 6 * q^5 - 6 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9 - 6 * q^10 - 18 * q^11 - 3 * q^12 - 10 * q^13 - 4 * q^14 - 18 * q^15 + q^16 - 6 * q^17 + 6 * q^18 + 2 * q^19 + 12 * q^20 + 24 * q^21 + 18 * q^23 - 5 * q^25 + 32 * q^26 + 27 * q^27 + 2 * q^28 + 36 * q^29 + 36 * q^30 - 4 * q^31 + q^32 + 27 * q^33 - 6 * q^34 + 6 * q^35 + 6 * q^36 - 4 * q^37 - 13 * q^38 - 42 * q^39 - 6 * q^40 - 6 * q^41 - 24 * q^42 - 28 * q^43 - 6 * q^47 - 6 * q^48 - 27 * q^49 - 41 * q^50 - 10 * q^52 - 48 * q^53 - 36 * q^54 - 18 * q^55 - 4 * q^56 - 9 * q^57 - 18 * q^58 + 9 * q^59 - 18 * q^60 - 10 * q^61 - 16 * q^62 - 6 * q^63 - 5 * q^64 + 6 * q^65 + 50 * q^67 - 15 * q^68 + 18 * q^69 + 42 * q^70 + 48 * q^71 + 24 * q^72 - 10 * q^73 + 26 * q^74 + 12 * q^75 + 23 * q^76 + 36 * q^77 + 36 * q^78 + 92 * q^79 + 12 * q^80 + 30 * q^82 + 12 * q^83 + 72 * q^85 + 26 * q^86 + 36 * q^87 + 27 * q^88 - 15 * q^89 + 18 * q^90 - 2 * q^91 - 6 * q^93 + 30 * q^94 + 6 * q^95 + 6 * q^96 + 20 * q^97 - 9 * q^98 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)

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
54.2.a	\(\chi_{54}(1, \cdot)\)	54.2.a.a	1	1
		54.2.a.b	1
54.2.c	\(\chi_{54}(19, \cdot)\)	54.2.c.a	2	2
54.2.e	\(\chi_{54}(7, \cdot)\)	54.2.e.a	6	6
		54.2.e.b	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

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