Space of modular forms of level 162 and weight 9

• Label: 162.9
• Level: 162
• Weight: 9
• Dimension: 1536
• Nonzero newspaces: 4
• Sturm bound: 13122
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(13122\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(162))\).

	Total	New	Old
Modular forms	5940	1536	4404
Cusp forms	5724	1536	4188
Eisenstein series	216	0	216

Trace form

1536 * q - 882 * q^5 + 5538 * q^7 - 10752 * q^10 + 45756 * q^11 - 47010 * q^13 - 94464 * q^14 + 274176 * q^18 - 1287720 * q^19 + 564480 * q^20 + 2721870 * q^21 + 432768 * q^22 - 2417130 * q^23 - 3077046 * q^25 + 3866562 * q^27 + 2835456 * q^28 + 8563554 * q^29 + 1292544 * q^30 - 4082634 * q^31 - 12138714 * q^33 + 930048 * q^34 + 24901668 * q^35 + 9112320 * q^36 + 310452 * q^37 - 26812800 * q^38 + 1376256 * q^40 + 22128480 * q^41 + 293184 * q^43 + 37896768 * q^45 - 7417344 * q^46 + 4632930 * q^47 - 32417574 * q^49 + 27744768 * q^50 - 54355896 * q^51 + 6017280 * q^52 + 46682604 * q^55 - 12091392 * q^56 + 65747808 * q^57 + 21354240 * q^58 + 79170120 * q^59 - 72977202 * q^61 - 101958480 * q^63 - 50331648 * q^64 - 6305058 * q^65 + 297787392 * q^66 - 83055708 * q^67 + 2458368 * q^68 - 398223792 * q^69 + 181798656 * q^70 - 251437608 * q^71 - 182845440 * q^72 + 29703630 * q^73 + 112151808 * q^74 + 492187500 * q^75 - 114868992 * q^76 + 583530174 * q^77 + 478734336 * q^78 - 193129518 * q^79 - 296732016 * q^81 + 44018688 * q^82 - 254457126 * q^83 - 196816896 * q^84 + 468568404 * q^85 - 388996992 * q^86 - 122724000 * q^87 - 55394304 * q^88 + 764382906 * q^89 + 1128960000 * q^90 - 367342590 * q^91 + 432693504 * q^92 + 497955456 * q^93 + 279518976 * q^94 + 169987104 * q^95 - 264241152 * q^96 + 809887524 * q^97 - 234233856 * q^98 + 1648813176 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(162))\)

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
162.9.b	\(\chi_{162}(161, \cdot)\)	162.9.b.a	8	1
		162.9.b.b	8
		162.9.b.c	16
162.9.d	\(\chi_{162}(53, \cdot)\)	162.9.d.a	4	2
		162.9.d.b	4
		162.9.d.c	4
		162.9.d.d	4
		162.9.d.e	8
		162.9.d.f	8
		162.9.d.g	16
		162.9.d.h	16
162.9.f	\(\chi_{162}(17, \cdot)\)	n/a	144	6
162.9.h	\(\chi_{162}(5, \cdot)\)	n/a	1296	18

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

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