Space of modular forms of level 162 and weight 2

• Label: 162.2
• Level: 162
• Weight: 2
• Dimension: 192
• Nonzero newspaces: 4
• Newform subspaces: 12
• Sturm bound: 2916
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(2916\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(162))\).

	Total	New	Old
Modular forms	837	192	645
Cusp forms	622	192	430
Eisenstein series	215	0	215

Trace form

192 * q + 6 * q^5 + 6 * q^7 + 3 * q^8 + 6 * q^10 + 15 * q^11 + 12 * q^13 + 6 * q^14 + 12 * q^17 - 9 * q^18 - 18 * q^19 - 30 * q^20 - 54 * q^21 - 21 * q^22 - 78 * q^23 - 36 * q^25 - 90 * q^26 - 54 * q^27 - 24 * q^28 - 84 * q^29 - 54 * q^30 - 36 * q^31 - 54 * q^33 - 15 * q^34 - 60 * q^35 - 18 * q^36 - 6 * q^37 + 3 * q^38 + 6 * q^40 - 3 * q^41 + 9 * q^43 + 6 * q^44 - 54 * q^45 + 12 * q^46 - 54 * q^47 - 12 * q^49 + 36 * q^50 - 63 * q^51 + 12 * q^52 - 30 * q^53 - 36 * q^55 + 6 * q^56 - 54 * q^57 + 24 * q^58 - 69 * q^59 - 18 * q^61 + 24 * q^62 - 54 * q^63 + 3 * q^64 + 12 * q^65 + 72 * q^66 - 45 * q^67 + 30 * q^68 + 126 * q^69 - 24 * q^70 + 120 * q^71 + 72 * q^72 + 42 * q^73 + 114 * q^74 + 180 * q^75 - 15 * q^76 + 246 * q^77 + 144 * q^78 - 60 * q^79 + 24 * q^80 + 144 * q^81 + 6 * q^82 + 144 * q^83 + 36 * q^84 - 36 * q^85 + 117 * q^86 + 288 * q^87 - 21 * q^88 + 174 * q^89 + 144 * q^90 + 30 * q^91 + 66 * q^92 + 126 * q^93 - 18 * q^94 + 84 * q^95 + 18 * q^96 - 15 * q^97 + 87 * q^98 + 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)

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
162.2.a	\(\chi_{162}(1, \cdot)\)	162.2.a.a	1	1
		162.2.a.b	1
		162.2.a.c	1
		162.2.a.d	1
162.2.c	\(\chi_{162}(55, \cdot)\)	162.2.c.a	2	2
		162.2.c.b	2
		162.2.c.c	2
		162.2.c.d	2
162.2.e	\(\chi_{162}(19, \cdot)\)	162.2.e.a	6	6
		162.2.e.b	12
162.2.g	\(\chi_{162}(7, \cdot)\)	162.2.g.a	72	18
		162.2.g.b	90

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)