Space of modular forms of level 144 and weight 5

• Label: 144.5
• Level: 144
• Weight: 5
• Dimension: 1006
• Nonzero newspaces: 8
• Newform subspaces: 23
• Sturm bound: 5760
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 23 \)
Sturm bound:			\(5760\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(144))\).

	Total	New	Old
Modular forms	2416	1046	1370
Cusp forms	2192	1006	1186
Eisenstein series	224	40	184

Trace form

1006 * q - 6 * q^2 - 6 * q^3 - 12 * q^4 + 27 * q^5 - 8 * q^6 - 39 * q^7 - 96 * q^8 + 110 * q^9 - 116 * q^10 + 93 * q^11 - 8 * q^12 - 3 * q^13 + 168 * q^14 - 261 * q^15 + 1732 * q^16 + 24 * q^17 - 1108 * q^18 - 590 * q^19 - 3312 * q^20 - 1145 * q^21 - 1168 * q^22 + 1155 * q^23 + 1496 * q^24 + 1716 * q^25 + 4836 * q^26 + 1866 * q^27 + 3640 * q^28 + 1179 * q^29 + 2084 * q^30 + 1709 * q^31 - 2916 * q^32 - 4803 * q^33 - 1824 * q^34 + 6336 * q^35 - 7500 * q^36 + 174 * q^37 + 1044 * q^38 + 2505 * q^39 + 8740 * q^40 + 321 * q^41 + 11792 * q^42 - 22469 * q^43 + 6216 * q^44 - 4299 * q^45 + 620 * q^46 - 10809 * q^47 - 4948 * q^48 + 6020 * q^49 - 8454 * q^50 + 20680 * q^51 - 4832 * q^52 + 20862 * q^53 - 18180 * q^54 + 27922 * q^55 - 38880 * q^56 - 14452 * q^57 - 5916 * q^58 - 23379 * q^59 + 16948 * q^60 - 18115 * q^61 + 41784 * q^62 - 10011 * q^63 - 24024 * q^64 + 4377 * q^65 + 64192 * q^66 - 17029 * q^67 + 39888 * q^68 + 6329 * q^69 + 8620 * q^70 + 19956 * q^71 - 16024 * q^72 + 18816 * q^73 - 47136 * q^74 + 5266 * q^75 + 6480 * q^76 + 2781 * q^77 - 104972 * q^78 - 15715 * q^79 - 103680 * q^80 - 32738 * q^81 + 44856 * q^82 - 4083 * q^83 + 30088 * q^84 - 44016 * q^85 + 112176 * q^86 + 41403 * q^87 + 47668 * q^88 + 7092 * q^89 + 108280 * q^90 - 2002 * q^91 + 67212 * q^92 - 23433 * q^93 + 18252 * q^94 - 27942 * q^95 - 12996 * q^96 - 7961 * q^97 - 69210 * q^98 - 55845 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.5.b	\(\chi_{144}(55, \cdot)\)	None	0	1
144.5.e	\(\chi_{144}(17, \cdot)\)	144.5.e.a	2	1
		144.5.e.b	2
		144.5.e.c	2
		144.5.e.d	2
144.5.g	\(\chi_{144}(127, \cdot)\)	144.5.g.a	1	1
		144.5.g.b	1
		144.5.g.c	2
		144.5.g.d	2
		144.5.g.e	2
		144.5.g.f	2
144.5.h	\(\chi_{144}(89, \cdot)\)	None	0	1
144.5.j	\(\chi_{144}(53, \cdot)\)	144.5.j.a	64	2
144.5.m	\(\chi_{144}(19, \cdot)\)	144.5.m.a	14	2
		144.5.m.b	32
		144.5.m.c	32
144.5.n	\(\chi_{144}(41, \cdot)\)	None	0	2
144.5.o	\(\chi_{144}(31, \cdot)\)	144.5.o.a	16	2
		144.5.o.b	16
		144.5.o.c	16
144.5.q	\(\chi_{144}(65, \cdot)\)	144.5.q.a	6	2
		144.5.q.b	8
		144.5.q.c	8
		144.5.q.d	24
144.5.t	\(\chi_{144}(7, \cdot)\)	None	0	2
144.5.v	\(\chi_{144}(43, \cdot)\)	144.5.v.a	376	4
144.5.w	\(\chi_{144}(5, \cdot)\)	144.5.w.a	376	4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

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