Space of modular forms of level 162 and weight 4

• Label: 162.4
• Level: 162
• Weight: 4
• Dimension: 576
• Nonzero newspaces: 4
• Newform subspaces: 22
• Sturm bound: 5832
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(5832\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(162))\).

	Total	New	Old
Modular forms	2295	576	1719
Cusp forms	2079	576	1503
Eisenstein series	216	0	216

Trace form

576 * q + 24 * q^5 - 36 * q^7 - 24 * q^8 - 36 * q^10 + 51 * q^11 + 90 * q^13 + 132 * q^14 - 204 * q^17 - 414 * q^18 - 810 * q^19 - 480 * q^20 - 216 * q^21 + 126 * q^22 + 1416 * q^23 + 1242 * q^25 + 2340 * q^26 + 1404 * q^27 + 576 * q^28 + 1842 * q^29 + 756 * q^30 + 162 * q^31 - 864 * q^33 - 234 * q^34 - 3732 * q^35 - 1152 * q^36 - 2070 * q^37 - 1626 * q^38 - 144 * q^40 - 3873 * q^41 - 2079 * q^43 - 264 * q^44 - 1026 * q^45 - 504 * q^46 + 432 * q^47 + 1530 * q^49 + 792 * q^50 + 2961 * q^51 + 360 * q^52 + 6450 * q^53 + 4320 * q^55 + 528 * q^56 + 2214 * q^57 + 72 * q^58 + 1911 * q^59 - 972 * q^61 - 1488 * q^62 - 1998 * q^63 + 576 * q^64 - 2130 * q^65 + 9360 * q^66 - 7749 * q^67 + 336 * q^68 + 4122 * q^69 - 1368 * q^70 + 1200 * q^71 - 576 * q^72 + 1692 * q^73 - 2388 * q^74 - 9000 * q^75 + 1980 * q^76 - 9276 * q^77 - 10656 * q^78 + 8190 * q^79 - 1920 * q^80 - 11520 * q^81 + 1044 * q^82 - 5958 * q^83 - 2448 * q^84 + 6480 * q^85 - 3582 * q^86 - 10944 * q^87 + 504 * q^88 - 7224 * q^89 + 1440 * q^90 - 6876 * q^91 + 1488 * q^92 + 9090 * q^93 - 6156 * q^94 + 2172 * q^95 + 2880 * q^96 - 9441 * q^97 + 10914 * q^98 + 20754 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(162))\)

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
162.4.a	\(\chi_{162}(1, \cdot)\)	162.4.a.a	1	1
		162.4.a.b	1
		162.4.a.c	1
		162.4.a.d	1
		162.4.a.e	2
		162.4.a.f	2
		162.4.a.g	2
		162.4.a.h	2
162.4.c	\(\chi_{162}(55, \cdot)\)	162.4.c.a	2	2
		162.4.c.b	2
		162.4.c.c	2
		162.4.c.d	2
		162.4.c.e	2
		162.4.c.f	2
		162.4.c.g	2
		162.4.c.h	2
		162.4.c.i	4
		162.4.c.j	4
162.4.e	\(\chi_{162}(19, \cdot)\)	162.4.e.a	24	6
		162.4.e.b	30
162.4.g	\(\chi_{162}(7, \cdot)\)	162.4.g.a	234	18
		162.4.g.b	252

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

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