Space of modular forms of level 144 and weight 4

• Label: 144.4
• Level: 144
• Weight: 4
• Dimension: 749
• Nonzero newspaces: 8
• Newform subspaces: 26
• Sturm bound: 4608
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(4608\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(144))\).

	Total	New	Old
Modular forms	1840	790	1050
Cusp forms	1616	749	867
Eisenstein series	224	41	183

Trace form

749 * q - 6 * q^2 - 6 * q^3 + 4 * q^4 - 7 * q^5 - 8 * q^6 + 9 * q^7 - 48 * q^8 - 22 * q^9 - 84 * q^10 - 75 * q^11 - 8 * q^12 - 57 * q^13 + 120 * q^14 - 27 * q^15 - 252 * q^16 - 116 * q^17 - 148 * q^18 + 122 * q^19 + 416 * q^20 + 289 * q^21 + 416 * q^22 + 319 * q^23 + 728 * q^24 + 675 * q^25 + 820 * q^26 - 384 * q^27 + 408 * q^28 - 287 * q^29 - 508 * q^30 + 111 * q^31 - 996 * q^32 - 63 * q^33 - 960 * q^34 - 558 * q^35 + 756 * q^36 - 960 * q^37 + 1172 * q^38 - 231 * q^39 - 764 * q^40 - 117 * q^41 - 688 * q^42 + 1477 * q^43 - 2216 * q^44 - 273 * q^45 - 1828 * q^46 + 3813 * q^47 - 2452 * q^48 + 1477 * q^49 - 3606 * q^50 + 1954 * q^51 - 1968 * q^52 - 626 * q^53 - 228 * q^54 - 2006 * q^55 + 2880 * q^56 + 1148 * q^57 + 2260 * q^58 - 4345 * q^59 + 7924 * q^60 - 1161 * q^61 + 4728 * q^62 - 2547 * q^63 + 1576 * q^64 - 1899 * q^65 - 4928 * q^66 + 2843 * q^67 - 3440 * q^68 - 2863 * q^69 + 3468 * q^70 + 1784 * q^71 - 7960 * q^72 + 5862 * q^73 - 4096 * q^74 - 530 * q^75 + 1216 * q^76 - 5323 * q^77 - 524 * q^78 - 1159 * q^79 + 6688 * q^80 - 494 * q^81 + 3432 * q^82 - 1521 * q^83 + 9544 * q^84 - 5330 * q^85 + 8800 * q^86 - 249 * q^87 - 4812 * q^88 + 804 * q^89 + 1144 * q^90 - 5370 * q^91 - 12500 * q^92 + 861 * q^93 - 12116 * q^94 - 1372 * q^95 - 6468 * q^96 + 2545 * q^97 - 14474 * q^98 - 1575 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.4.a	\(\chi_{144}(1, \cdot)\)	144.4.a.a	1	1
		144.4.a.b	1
		144.4.a.c	1
		144.4.a.d	1
		144.4.a.e	1
		144.4.a.f	1
		144.4.a.g	1
144.4.c	\(\chi_{144}(143, \cdot)\)	144.4.c.a	2	1
		144.4.c.b	4
144.4.d	\(\chi_{144}(73, \cdot)\)	None	0	1
144.4.f	\(\chi_{144}(71, \cdot)\)	None	0	1
144.4.i	\(\chi_{144}(49, \cdot)\)	144.4.i.a	2	2
		144.4.i.b	4
		144.4.i.c	4
		144.4.i.d	6
		144.4.i.e	8
		144.4.i.f	10
144.4.k	\(\chi_{144}(37, \cdot)\)	144.4.k.a	10	2
		144.4.k.b	24
		144.4.k.c	24
144.4.l	\(\chi_{144}(35, \cdot)\)	144.4.l.a	48	2
144.4.p	\(\chi_{144}(23, \cdot)\)	None	0	2
144.4.r	\(\chi_{144}(25, \cdot)\)	None	0	2
144.4.s	\(\chi_{144}(47, \cdot)\)	144.4.s.a	2	2
		144.4.s.b	2
		144.4.s.c	10
		144.4.s.d	10
		144.4.s.e	12
144.4.u	\(\chi_{144}(11, \cdot)\)	144.4.u.a	280	4
144.4.x	\(\chi_{144}(13, \cdot)\)	144.4.x.a	280	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

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