Space of modular forms of level 144 and weight 16

• Label: 144.16
• Level: 144
• Weight: 16
• Dimension: 3827
• Nonzero newspaces: 8
• Sturm bound: 18432
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(18432\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(144))\).

	Total	New	Old
Modular forms	8752	3868	4884
Cusp forms	8528	3827	4701
Eisenstein series	224	41	183

Trace form

3827 * q - 6 * q^2 - 6 * q^3 - 48956 * q^4 - 68387 * q^5 - 8 * q^6 - 3234663 * q^7 + 11363472 * q^8 - 7624102 * q^9 - 13284 * q^10 - 34705395 * q^11 - 8 * q^12 + 313369467 * q^13 - 815345544 * q^14 + 322926453 * q^15 - 7229386236 * q^16 + 3014492312 * q^17 - 15149322868 * q^18 - 610823806 * q^19 + 12500734816 * q^20 - 29145844943 * q^21 + 43206670640 * q^22 + 60358280111 * q^23 + 5486368472 * q^24 - 119539710675 * q^25 - 77965401916 * q^26 + 224736516624 * q^27 + 198208693272 * q^28 - 591966546475 * q^29 - 447817870588 * q^30 + 340778381583 * q^31 + 1015442180124 * q^32 - 1288385969679 * q^33 + 509322537984 * q^34 + 1139740552722 * q^35 - 276901896204 * q^36 + 493621951236 * q^37 - 8586570328508 * q^38 - 2270078836503 * q^39 + 8204664408196 * q^40 + 2794666913991 * q^41 - 9413855922928 * q^42 + 503109831949 * q^43 + 18406982587928 * q^44 + 6158632571727 * q^45 - 6481901190436 * q^46 + 40874243206821 * q^47 - 14332262782612 * q^48 - 43682696495669 * q^49 + 48494504493594 * q^50 - 9159756994862 * q^51 + 14493493503120 * q^52 + 5429785679474 * q^53 - 26555083743108 * q^54 - 78137510543846 * q^55 + 155405698156992 * q^56 - 30227303518996 * q^57 - 117168754690844 * q^58 + 3723577647151 * q^59 - 135266756420876 * q^60 - 78429891660597 * q^61 + 30156078377688 * q^62 + 39514411397133 * q^63 + 421533016290856 * q^64 - 306332181992019 * q^65 + 13975177142272 * q^66 - 252836211521341 * q^67 + 424280366820752 * q^68 + 308315335378481 * q^69 + 291868938641388 * q^70 - 696740004948248 * q^71 - 713220078453016 * q^72 + 213243224099298 * q^73 + 522312344954032 * q^74 + 116841476401390 * q^75 + 260745138610432 * q^76 - 463164012965867 * q^77 - 2606699778951116 * q^78 + 16803228349529 * q^79 + 1618324718292128 * q^80 + 1601740986576418 * q^81 - 3553467028501656 * q^82 + 381454064296263 * q^83 - 706587464837048 * q^84 - 471731748309050 * q^85 - 734701604881936 * q^86 - 92783929060329 * q^87 - 3133762865642700 * q^88 - 1345657521400848 * q^89 + 3980345323632184 * q^90 + 2768398019546886 * q^91 + 5500364749353644 * q^92 + 2331848572022589 * q^93 - 5684291524282772 * q^94 - 5548251366171932 * q^95 - 3688130170858308 * q^96 - 1022895716145107 * q^97 + 10252626012324278 * q^98 + 7751954471762745 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.16.a	\(\chi_{144}(1, \cdot)\)	144.16.a.a	1	1
		144.16.a.b	1
		144.16.a.c	1
		144.16.a.d	1
		144.16.a.e	1
		144.16.a.f	1
		144.16.a.g	1
		144.16.a.h	1
		144.16.a.i	1
		144.16.a.j	1
		144.16.a.k	1
		144.16.a.l	1
		144.16.a.m	1
		144.16.a.n	1
		144.16.a.o	1
		144.16.a.p	2
		144.16.a.q	2
		144.16.a.r	2
		144.16.a.s	2
		144.16.a.t	2
		144.16.a.u	2
		144.16.a.v	2
		144.16.a.w	4
		144.16.a.x	4
144.16.c	\(\chi_{144}(143, \cdot)\)	144.16.c.a	2	1
		144.16.c.b	8
		144.16.c.c	20
144.16.d	\(\chi_{144}(73, \cdot)\)	None	0	1
144.16.f	\(\chi_{144}(71, \cdot)\)	None	0	1
144.16.i	\(\chi_{144}(49, \cdot)\)	n/a	178	2
144.16.k	\(\chi_{144}(37, \cdot)\)	n/a	298	2
144.16.l	\(\chi_{144}(35, \cdot)\)	n/a	240	2
144.16.p	\(\chi_{144}(23, \cdot)\)	None	0	2
144.16.r	\(\chi_{144}(25, \cdot)\)	None	0	2
144.16.s	\(\chi_{144}(47, \cdot)\)	n/a	180	2
144.16.u	\(\chi_{144}(11, \cdot)\)	n/a	1432	4
144.16.x	\(\chi_{144}(13, \cdot)\)	n/a	1432	4

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

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