Space of modular forms of level 144 and weight 14

• Label: 144.14
• Level: 144
• Weight: 14
• Dimension: 3314
• Nonzero newspaces: 8
• Sturm bound: 16128
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(16128\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(144))\).

	Total	New	Old
Modular forms	7600	3355	4245
Cusp forms	7376	3314	4062
Eisenstein series	224	41	183

Trace form

3314 * q - 6 * q^2 - 6 * q^3 + 356 * q^4 + 16895 * q^5 - 8 * q^6 + 170065 * q^7 - 1076880 * q^8 - 654478 * q^9 + 1809788 * q^10 + 8858049 * q^11 - 8 * q^12 - 26529515 * q^13 - 32258280 * q^14 + 55638477 * q^15 - 107639932 * q^16 + 107619190 * q^17 + 279032012 * q^18 - 125579362 * q^19 + 662047232 * q^20 + 1352296825 * q^21 - 245445136 * q^22 - 1566413801 * q^23 - 1471252264 * q^24 + 8387636174 * q^25 + 8162154820 * q^26 - 4041096072 * q^27 - 15259830824 * q^28 - 7818134609 * q^29 + 24305053892 * q^30 - 5087335985 * q^31 - 57989085156 * q^32 + 5229943689 * q^33 + 92362998080 * q^34 - 26827960590 * q^35 - 52988607372 * q^36 - 43690694186 * q^37 - 44070632860 * q^38 + 167981400849 * q^39 + 134003381572 * q^40 - 109925867667 * q^41 + 100502772752 * q^42 + 229961706153 * q^43 - 384536924744 * q^44 + 50356969023 * q^45 + 262752377276 * q^46 - 776325213003 * q^47 + 376589703404 * q^48 - 558640238374 * q^49 - 827860714086 * q^50 + 813886285066 * q^51 - 708191383696 * q^52 + 277957136500 * q^53 + 1222777626876 * q^54 - 1501487093022 * q^55 - 804766582272 * q^56 - 1310883483004 * q^57 - 1806468905308 * q^58 - 212514757525 * q^59 - 1307332727180 * q^60 + 1094515784213 * q^61 - 2209368876648 * q^62 - 422071554243 * q^63 - 3660460917208 * q^64 + 1052336979177 * q^65 - 6274781161088 * q^66 + 2172782560975 * q^67 - 1839995159792 * q^68 + 610472444321 * q^69 - 5547262866452 * q^70 - 258741539728 * q^71 + 11259455066600 * q^72 + 4402925237800 * q^73 - 3103239757936 * q^74 - 4049057525714 * q^75 + 1740941554016 * q^76 - 6634014256891 * q^77 + 9907573819828 * q^78 + 2372403471113 * q^79 + 47902984357600 * q^80 + 3806945302090 * q^81 - 4434905282360 * q^82 - 29721174668613 * q^83 - 41857327044152 * q^84 - 5481967356878 * q^85 + 69865528015024 * q^86 + 16730991667983 * q^87 + 18197696409140 * q^88 - 11928882453090 * q^89 - 17252494498376 * q^90 - 58761865668794 * q^91 - 36327472446740 * q^92 + 12821905432749 * q^93 + 41565480518828 * q^94 + 105277263575588 * q^95 + 41983271057340 * q^96 - 18815265826525 * q^97 - 21943423046186 * q^98 - 48339313529751 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.14.a	\(\chi_{144}(1, \cdot)\)	144.14.a.a	1	1
		144.14.a.b	1
		144.14.a.c	1
		144.14.a.d	1
		144.14.a.e	1
		144.14.a.f	1
		144.14.a.g	1
		144.14.a.h	1
		144.14.a.i	1
		144.14.a.j	1
		144.14.a.k	1
		144.14.a.l	1
		144.14.a.m	2
		144.14.a.n	2
		144.14.a.o	2
		144.14.a.p	2
		144.14.a.q	2
		144.14.a.r	2
		144.14.a.s	2
		144.14.a.t	3
		144.14.a.u	3
144.14.c	\(\chi_{144}(143, \cdot)\)	144.14.c.a	2	1
		144.14.c.b	8
		144.14.c.c	16
144.14.d	\(\chi_{144}(73, \cdot)\)	None	0	1
144.14.f	\(\chi_{144}(71, \cdot)\)	None	0	1
144.14.i	\(\chi_{144}(49, \cdot)\)	n/a	154	2
144.14.k	\(\chi_{144}(37, \cdot)\)	n/a	258	2
144.14.l	\(\chi_{144}(35, \cdot)\)	n/a	208	2
144.14.p	\(\chi_{144}(23, \cdot)\)	None	0	2
144.14.r	\(\chi_{144}(25, \cdot)\)	None	0	2
144.14.s	\(\chi_{144}(47, \cdot)\)	n/a	156	2
144.14.u	\(\chi_{144}(11, \cdot)\)	n/a	1240	4
144.14.x	\(\chi_{144}(13, \cdot)\)	n/a	1240	4

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)