Properties

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

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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

\( 3827 q - 6 q^{2} - 6 q^{3} - 48956 q^{4} - 68387 q^{5} - 8 q^{6} - 3234663 q^{7} + 11363472 q^{8} - 7624102 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

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 the 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

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