Space of modular forms of level 18 and weight 2

• Label: 18.2
• Level: 18
• Weight: 2
• Dimension: 2
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 36
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(18))\).

	Total	New	Old
Modular forms	17	2	15
Cusp forms	2	2	0
Eisenstein series	15	0	15

Trace form

2 * q - q^2 - 3 * q^3 - q^4 + 3 * q^6 - 2 * q^7 + 2 * q^8 + 3 * q^9 + 3 * q^11 - 2 * q^13 - 2 * q^14 - q^16 - 6 * q^17 - 6 * q^18 - 2 * q^19 + 6 * q^21 + 3 * q^22 + 6 * q^23 - 3 * q^24 + 5 * q^25 + 4 * q^26 + 4 * q^28 - 6 * q^29 + 4 * q^31 - q^32 - 9 * q^33 + 3 * q^34 + 3 * q^36 - 8 * q^37 + q^38 - 9 * q^41 + q^43 - 6 * q^44 - 12 * q^46 + 6 * q^47 + 3 * q^48 + 3 * q^49 + 5 * q^50 + 9 * q^51 - 2 * q^52 + 24 * q^53 + 9 * q^54 - 2 * q^56 + 3 * q^57 - 6 * q^58 - 3 * q^59 - 8 * q^61 - 8 * q^62 - 12 * q^63 + 2 * q^64 - 5 * q^67 + 3 * q^68 - 24 * q^71 + 3 * q^72 + 22 * q^73 + 4 * q^74 - 15 * q^75 + q^76 + 6 * q^77 - 6 * q^78 + 4 * q^79 - 9 * q^81 + 18 * q^82 - 12 * q^83 - 6 * q^84 + q^86 + 18 * q^87 + 3 * q^88 + 12 * q^89 + 8 * q^91 + 6 * q^92 + 6 * q^94 - 5 * q^97 - 6 * q^98 + 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.2.a	\(\chi_{18}(1, \cdot)\)	None	0	1
18.2.c	\(\chi_{18}(7, \cdot)\)	18.2.c.a	2	2