Space of modular forms of level 144 and weight 9

• Label: 144.9
• Level: 144
• Weight: 9
• Dimension: 2032
• Nonzero newspaces: 8
• Sturm bound: 10368
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(10368\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(144))\).

	Total	New	Old
Modular forms	4720	2072	2648
Cusp forms	4496	2032	2464
Eisenstein series	224	40	184

Trace form

2032 * q - 6 * q^2 - 6 * q^3 + 180 * q^4 - 513 * q^5 - 8 * q^6 + 3001 * q^7 - 8736 * q^8 + 3806 * q^9 - 1876 * q^10 - 19779 * q^11 - 8 * q^12 - 68543 * q^13 - 56856 * q^14 + 91899 * q^15 - 179260 * q^16 - 181956 * q^17 + 579692 * q^18 + 296818 * q^19 - 973872 * q^20 - 676841 * q^21 - 832688 * q^22 - 845565 * q^23 + 1589720 * q^24 + 1249706 * q^25 + 3918468 * q^26 - 1316454 * q^27 - 4421960 * q^28 - 934785 * q^29 - 3620956 * q^30 + 602461 * q^31 + 7369884 * q^32 - 532083 * q^33 - 3001120 * q^34 + 3551616 * q^35 + 973236 * q^36 + 2334514 * q^37 + 4204404 * q^38 + 14329497 * q^39 - 27838300 * q^40 - 8799483 * q^41 - 554608 * q^42 - 14953349 * q^43 + 39046920 * q^44 - 976779 * q^45 + 25094188 * q^46 + 20714391 * q^47 - 21819988 * q^48 + 10368150 * q^49 - 78403494 * q^50 + 24014488 * q^51 - 16722592 * q^52 + 12921282 * q^53 + 42722364 * q^54 - 43568078 * q^55 + 59135904 * q^56 + 12025628 * q^57 - 67832316 * q^58 + 83437149 * q^59 - 79259852 * q^60 - 38989375 * q^61 - 72099336 * q^62 - 102399531 * q^63 + 128508456 * q^64 + 23168577 * q^65 + 175715392 * q^66 + 49492731 * q^67 + 211189968 * q^68 + 221517689 * q^69 - 24441620 * q^70 - 79832076 * q^71 - 161457304 * q^72 + 13852036 * q^73 - 363476352 * q^74 - 149718734 * q^75 - 26712432 * q^76 + 27332541 * q^77 - 93787532 * q^78 + 208545085 * q^79 + 801982080 * q^80 + 405240910 * q^81 - 63910664 * q^82 - 209952483 * q^83 - 360758648 * q^84 + 72851624 * q^85 - 925798896 * q^86 - 356528517 * q^87 - 44616652 * q^88 + 135861480 * q^89 + 781008760 * q^90 + 402363502 * q^91 + 644375052 * q^92 - 128911113 * q^93 + 71235660 * q^94 + 476132538 * q^95 - 234420420 * q^96 + 357892059 * q^97 - 526340250 * q^98 - 546769989 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.9.b	\(\chi_{144}(55, \cdot)\)	None	0	1
144.9.e	\(\chi_{144}(17, \cdot)\)	144.9.e.a	2	1
		144.9.e.b	2
		144.9.e.c	2
		144.9.e.d	2
		144.9.e.e	4
		144.9.e.f	4
144.9.g	\(\chi_{144}(127, \cdot)\)	144.9.g.a	1	1
		144.9.g.b	1
		144.9.g.c	2
		144.9.g.d	2
		144.9.g.e	2
		144.9.g.f	2
		144.9.g.g	2
		144.9.g.h	4
		144.9.g.i	4
144.9.h	\(\chi_{144}(89, \cdot)\)	None	0	1
144.9.j	\(\chi_{144}(53, \cdot)\)	n/a	128	2
144.9.m	\(\chi_{144}(19, \cdot)\)	n/a	158	2
144.9.n	\(\chi_{144}(41, \cdot)\)	None	0	2
144.9.o	\(\chi_{144}(31, \cdot)\)	144.9.o.a	32	2
		144.9.o.b	32
		144.9.o.c	32
144.9.q	\(\chi_{144}(65, \cdot)\)	144.9.q.a	14	2
		144.9.q.b	16
		144.9.q.c	16
		144.9.q.d	48
144.9.t	\(\chi_{144}(7, \cdot)\)	None	0	2
144.9.v	\(\chi_{144}(43, \cdot)\)	n/a	760	4
144.9.w	\(\chi_{144}(5, \cdot)\)	n/a	760	4

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)