Space of modular forms of level 144 and weight 2

• Label: 144.2
• Level: 144
• Weight: 2
• Dimension: 236
• Nonzero newspaces: 8
• Newform subspaces: 22
• Sturm bound: 2304
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(2304\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(144))\).

	Total	New	Old
Modular forms	688	277	411
Cusp forms	465	236	229
Eisenstein series	223	41	182

Trace form

236 * q - 6 * q^2 - 6 * q^3 - 4 * q^4 - 5 * q^5 - 8 * q^6 + q^7 + 2 * q^9 - 16 * q^10 + 9 * q^11 - 8 * q^12 + q^13 - 24 * q^14 - 3 * q^15 - 28 * q^16 - 22 * q^17 - 28 * q^18 - 10 * q^19 - 56 * q^20 - 23 * q^21 - 52 * q^22 - 25 * q^23 - 40 * q^24 - 28 * q^25 - 64 * q^26 - 24 * q^27 - 56 * q^28 - 37 * q^29 - 28 * q^30 - 17 * q^31 - 36 * q^32 - 39 * q^33 - 16 * q^34 - 78 * q^35 - 12 * q^36 - 14 * q^37 + 40 * q^38 - 63 * q^39 + 52 * q^40 - 15 * q^41 + 32 * q^42 - 63 * q^43 + 80 * q^44 - 33 * q^45 + 44 * q^46 - 75 * q^47 + 44 * q^48 + 20 * q^49 + 78 * q^50 - 38 * q^51 + 56 * q^52 - 16 * q^53 + 36 * q^54 - 78 * q^55 + 96 * q^56 + 20 * q^57 + 32 * q^58 - 29 * q^59 + 100 * q^60 - 31 * q^61 + 96 * q^62 - 3 * q^63 - 88 * q^64 + 81 * q^65 + 112 * q^66 + 7 * q^67 + 80 * q^68 + 65 * q^69 - 44 * q^70 + 64 * q^71 + 104 * q^72 - 20 * q^73 + 52 * q^74 + 46 * q^75 - 40 * q^76 + 37 * q^77 + 100 * q^78 + 41 * q^79 + 128 * q^80 + 58 * q^81 - 8 * q^82 + 99 * q^83 + 136 * q^84 - 38 * q^85 + 140 * q^86 + 63 * q^87 + 68 * q^88 + 18 * q^89 + 136 * q^90 + 70 * q^91 + 92 * q^92 - 51 * q^93 + 92 * q^94 + 100 * q^95 + 60 * q^96 - 25 * q^97 + 86 * q^98 + 9 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.2.a	\(\chi_{144}(1, \cdot)\)	144.2.a.a	1	1
		144.2.a.b	1
144.2.c	\(\chi_{144}(143, \cdot)\)	144.2.c.a	2	1
144.2.d	\(\chi_{144}(73, \cdot)\)	None	0	1
144.2.f	\(\chi_{144}(71, \cdot)\)	None	0	1
144.2.i	\(\chi_{144}(49, \cdot)\)	144.2.i.a	2	2
		144.2.i.b	2
		144.2.i.c	2
		144.2.i.d	4
144.2.k	\(\chi_{144}(37, \cdot)\)	144.2.k.a	2	2
		144.2.k.b	8
		144.2.k.c	8
144.2.l	\(\chi_{144}(35, \cdot)\)	144.2.l.a	16	2
144.2.p	\(\chi_{144}(23, \cdot)\)	None	0	2
144.2.r	\(\chi_{144}(25, \cdot)\)	None	0	2
144.2.s	\(\chi_{144}(47, \cdot)\)	144.2.s.a	2	2
		144.2.s.b	2
		144.2.s.c	2
		144.2.s.d	2
		144.2.s.e	4
144.2.u	\(\chi_{144}(11, \cdot)\)	144.2.u.a	88	4
144.2.x	\(\chi_{144}(13, \cdot)\)	144.2.x.a	4	4
		144.2.x.b	4
		144.2.x.c	4
		144.2.x.d	4
		144.2.x.e	72

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

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