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