Space of modular forms of level 144 and weight 3

• Label: 144.3
• Level: 144
• Weight: 3
• Dimension: 493
• Nonzero newspaces: 8
• Newform subspaces: 19
• Sturm bound: 3456
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(3456\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(144))\).

	Total	New	Old
Modular forms	1264	533	731
Cusp forms	1040	493	547
Eisenstein series	224	40	184

Trace form

493 * q - 6 * q^2 - 6 * q^3 - 12 * q^4 - 15 * q^5 - 8 * q^6 - 23 * q^7 - 10 * q^9 + 20 * q^10 - 19 * q^11 - 8 * q^12 + 19 * q^13 + 40 * q^14 + 27 * q^15 + 68 * q^16 + 102 * q^17 + 92 * q^18 + 82 * q^19 + 80 * q^20 + 31 * q^21 - 8 * q^22 + 67 * q^23 - 40 * q^24 - 79 * q^25 - 100 * q^26 + 66 * q^27 - 200 * q^28 - 127 * q^29 - 220 * q^30 - 107 * q^31 - 356 * q^32 - 75 * q^33 - 256 * q^34 + 96 * q^35 - 204 * q^36 + 52 * q^37 - 468 * q^38 + 129 * q^39 - 412 * q^40 + 15 * q^41 - 208 * q^42 + 283 * q^43 - 248 * q^44 - 171 * q^45 - 20 * q^46 - 225 * q^47 + 44 * q^48 - 117 * q^49 + 322 * q^50 - 320 * q^51 + 416 * q^52 - 124 * q^53 + 300 * q^54 - 446 * q^55 + 352 * q^56 - 316 * q^57 + 732 * q^58 - 587 * q^59 - 524 * q^60 + 83 * q^61 - 216 * q^62 - 339 * q^63 + 552 * q^64 - 59 * q^65 - 608 * q^66 - 69 * q^67 + 80 * q^68 - 103 * q^69 + 28 * q^70 - 268 * q^71 + 104 * q^72 - 146 * q^73 + 72 * q^74 - 62 * q^75 - 432 * q^76 + 173 * q^77 + 532 * q^78 - 563 * q^79 - 192 * q^80 + 646 * q^81 - 1544 * q^82 - 283 * q^83 + 520 * q^84 + 308 * q^85 - 72 * q^86 - 69 * q^87 - 844 * q^88 + 426 * q^89 + 280 * q^90 + 142 * q^91 - 500 * q^92 + 567 * q^93 - 84 * q^94 + 714 * q^95 + 60 * q^96 + 429 * q^97 + 838 * q^98 + 747 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.3.b	\(\chi_{144}(55, \cdot)\)	None	0	1
144.3.e	\(\chi_{144}(17, \cdot)\)	144.3.e.a	2	1
		144.3.e.b	2
144.3.g	\(\chi_{144}(127, \cdot)\)	144.3.g.a	1	1
		144.3.g.b	2
		144.3.g.c	2
144.3.h	\(\chi_{144}(89, \cdot)\)	None	0	1
144.3.j	\(\chi_{144}(53, \cdot)\)	144.3.j.a	32	2
144.3.m	\(\chi_{144}(19, \cdot)\)	144.3.m.a	6	2
		144.3.m.b	16
		144.3.m.c	16
144.3.n	\(\chi_{144}(41, \cdot)\)	None	0	2
144.3.o	\(\chi_{144}(31, \cdot)\)	144.3.o.a	8	2
		144.3.o.b	8
		144.3.o.c	8
144.3.q	\(\chi_{144}(65, \cdot)\)	144.3.q.a	2	2
		144.3.q.b	4
		144.3.q.c	4
		144.3.q.d	4
		144.3.q.e	8
144.3.t	\(\chi_{144}(7, \cdot)\)	None	0	2
144.3.v	\(\chi_{144}(43, \cdot)\)	144.3.v.a	184	4
144.3.w	\(\chi_{144}(5, \cdot)\)	144.3.w.a	184	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

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