Space of modular forms of level 18 and weight 3

• Label: 18.3
• Level: 18
• Weight: 3
• Dimension: 6
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 54
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(54\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(18))\).

	Total	New	Old
Modular forms	26	6	20
Cusp forms	10	6	4
Eisenstein series	16	0	16

Trace form

6 * q - 18 * q^5 - 12 * q^6 - 6 * q^7 + 12 * q^9 + 12 * q^10 + 18 * q^11 + 12 * q^12 + 6 * q^13 + 36 * q^14 + 18 * q^15 - 24 * q^18 - 72 * q^19 - 36 * q^20 - 42 * q^21 - 60 * q^22 + 18 * q^23 + 18 * q^25 + 24 * q^28 + 18 * q^29 + 72 * q^30 + 126 * q^31 + 54 * q^33 + 60 * q^34 + 12 * q^36 + 60 * q^37 - 72 * q^38 - 102 * q^39 - 24 * q^40 - 126 * q^41 - 48 * q^42 - 126 * q^43 - 54 * q^45 + 24 * q^46 + 54 * q^47 + 24 * q^48 - 78 * q^49 - 72 * q^51 - 12 * q^52 + 36 * q^54 + 36 * q^55 + 72 * q^56 + 144 * q^57 + 12 * q^58 + 126 * q^59 - 36 * q^60 + 162 * q^61 + 222 * q^63 - 48 * q^64 + 90 * q^65 - 72 * q^66 - 90 * q^67 + 72 * q^68 + 18 * q^69 - 156 * q^70 - 96 * q^72 - 240 * q^73 + 72 * q^74 - 12 * q^75 + 24 * q^76 - 90 * q^77 + 144 * q^78 - 138 * q^79 - 252 * q^81 + 12 * q^82 - 378 * q^83 - 144 * q^84 - 108 * q^86 - 54 * q^87 + 120 * q^88 + 348 * q^91 + 36 * q^92 + 222 * q^93 + 324 * q^94 + 180 * q^95 + 48 * q^96 + 366 * q^97 + 126 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.3.b	\(\chi_{18}(17, \cdot)\)	18.3.b.a	2	1
18.3.d	\(\chi_{18}(5, \cdot)\)	18.3.d.a	4	2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

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