Space of modular forms of level 144 and weight 8

• Label: 144.8
• Level: 144
• Weight: 8
• Dimension: 1775
• Nonzero newspaces: 8
• Sturm bound: 9216
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(9216\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(144))\).

	Total	New	Old
Modular forms	4144	1816	2328
Cusp forms	3920	1775	2145
Eisenstein series	224	41	183

Trace form

1775 * q - 6 * q^2 - 6 * q^3 - 188 * q^4 + 133 * q^5 - 8 * q^6 - 1351 * q^7 - 1008 * q^8 + 2234 * q^9 + 12956 * q^10 - 10179 * q^11 - 8 * q^12 + 3779 * q^13 + 21240 * q^14 + 16533 * q^15 + 65540 * q^16 + 35216 * q^17 - 42868 * q^18 + 60434 * q^19 - 302624 * q^20 + 6865 * q^21 + 332592 * q^22 - 6001 * q^23 + 335576 * q^24 + 161425 * q^25 - 620092 * q^26 + 247728 * q^27 - 920808 * q^28 - 571747 * q^29 + 137732 * q^30 + 455887 * q^31 + 1888284 * q^32 + 460497 * q^33 - 396032 * q^34 + 27282 * q^35 + 299508 * q^36 + 572780 * q^37 - 3826748 * q^38 - 628215 * q^39 + 1684356 * q^40 - 1369569 * q^41 + 2995472 * q^42 - 2463971 * q^43 - 558952 * q^44 + 2648847 * q^45 - 3096996 * q^46 + 7737765 * q^47 - 5044372 * q^48 - 2588601 * q^49 - 1778406 * q^50 - 1783118 * q^51 + 7969808 * q^52 + 1522970 * q^53 + 7445628 * q^54 - 7865606 * q^55 + 2628288 * q^56 + 2017100 * q^57 - 12561692 * q^58 + 4726399 * q^59 - 26449676 * q^60 + 2848083 * q^61 + 27430872 * q^62 + 1781133 * q^63 - 10529240 * q^64 + 18969501 * q^65 + 21033472 * q^66 - 272237 * q^67 - 12033136 * q^68 - 16758799 * q^69 - 7071252 * q^70 - 16470584 * q^71 - 38360344 * q^72 - 856390 * q^73 - 20947664 * q^74 + 11830510 * q^75 + 7947904 * q^76 + 34240213 * q^77 + 71195188 * q^78 - 9466599 * q^79 + 23565728 * q^80 + 20022466 * q^81 - 33584920 * q^82 - 31517001 * q^83 - 44863928 * q^84 - 24154570 * q^85 - 25777168 * q^86 + 20723511 * q^87 - 8857804 * q^88 + 8761320 * q^89 + 54130744 * q^90 + 28698886 * q^91 - 32760916 * q^92 + 56721405 * q^93 + 2505580 * q^94 - 91602332 * q^95 - 56434500 * q^96 - 1130491 * q^97 - 47532490 * q^98 - 68033799 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.8.a	\(\chi_{144}(1, \cdot)\)	144.8.a.a	1	1
		144.8.a.b	1
		144.8.a.c	1
		144.8.a.d	1
		144.8.a.e	1
		144.8.a.f	1
		144.8.a.g	1
		144.8.a.h	1
		144.8.a.i	1
		144.8.a.j	1
		144.8.a.k	1
		144.8.a.l	2
		144.8.a.m	2
		144.8.a.n	2
144.8.c	\(\chi_{144}(143, \cdot)\)	144.8.c.a	2	1
		144.8.c.b	4
		144.8.c.c	8
144.8.d	\(\chi_{144}(73, \cdot)\)	None	0	1
144.8.f	\(\chi_{144}(71, \cdot)\)	None	0	1
144.8.i	\(\chi_{144}(49, \cdot)\)	144.8.i.a	6	2
		144.8.i.b	8
		144.8.i.c	12
		144.8.i.d	14
		144.8.i.e	20
		144.8.i.f	22
144.8.k	\(\chi_{144}(37, \cdot)\)	n/a	138	2
144.8.l	\(\chi_{144}(35, \cdot)\)	n/a	112	2
144.8.p	\(\chi_{144}(23, \cdot)\)	None	0	2
144.8.r	\(\chi_{144}(25, \cdot)\)	None	0	2
144.8.s	\(\chi_{144}(47, \cdot)\)	144.8.s.a	28	2
		144.8.s.b	28
		144.8.s.c	28
144.8.u	\(\chi_{144}(11, \cdot)\)	n/a	664	4
144.8.x	\(\chi_{144}(13, \cdot)\)	n/a	664	4

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

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