Properties

 Label 336.6 Level 336 Weight 6 Dimension 6164 Nonzero newspaces 16 Sturm bound 36864 Trace bound 8

Defining parameters

 Level: $$N$$ = $$336 = 2^{4} \cdot 3 \cdot 7$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$16$$ Sturm bound: $$36864$$ Trace bound: $$8$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(336))$$.

Total New Old
Modular forms 15696 6256 9440
Cusp forms 15024 6164 8860
Eisenstein series 672 92 580

Trace form

 $$6164 q - 23 q^{3} - 104 q^{4} - 76 q^{5} + 220 q^{6} + 150 q^{7} + 984 q^{8} - 945 q^{9} + O(q^{10})$$ $$6164 q - 23 q^{3} - 104 q^{4} - 76 q^{5} + 220 q^{6} + 150 q^{7} + 984 q^{8} - 945 q^{9} - 1752 q^{10} - 3624 q^{11} + 4 q^{12} + 460 q^{13} - 324 q^{14} + 4482 q^{15} - 8376 q^{16} - 404 q^{17} + 8788 q^{18} - 9670 q^{19} + 15200 q^{20} - 8359 q^{21} - 2464 q^{22} - 2156 q^{23} - 15588 q^{24} + 20272 q^{25} + 25960 q^{26} + 10372 q^{27} + 1896 q^{28} + 28924 q^{29} + 1468 q^{30} - 53698 q^{31} - 88320 q^{32} - 43507 q^{33} - 62248 q^{34} - 31188 q^{35} + 64712 q^{36} + 31918 q^{37} + 144176 q^{38} + 112064 q^{39} + 180824 q^{40} + 21756 q^{41} - 90360 q^{42} - 92496 q^{43} - 145616 q^{44} + 5709 q^{45} + 56128 q^{46} + 27612 q^{47} + 210876 q^{48} + 593108 q^{49} - 107424 q^{50} - 71259 q^{51} + 31440 q^{52} + 13492 q^{53} - 394732 q^{54} + 52832 q^{55} - 340200 q^{56} - 162582 q^{57} - 244928 q^{58} + 17624 q^{59} + 118076 q^{60} + 36582 q^{61} + 237504 q^{62} + 102129 q^{63} + 106408 q^{64} + 445848 q^{65} + 284884 q^{66} - 269430 q^{67} + 399592 q^{68} - 391148 q^{69} - 420432 q^{70} - 253372 q^{71} - 302804 q^{72} - 270322 q^{73} + 189992 q^{74} + 400424 q^{75} - 484472 q^{76} - 35024 q^{77} - 426312 q^{78} + 414798 q^{79} - 1246736 q^{80} + 728015 q^{81} + 333752 q^{82} + 289800 q^{83} + 5084 q^{84} + 814732 q^{85} + 1162336 q^{86} - 448620 q^{87} + 1180008 q^{88} + 189564 q^{89} + 127364 q^{90} - 917028 q^{91} + 965080 q^{92} - 826523 q^{93} + 541832 q^{94} - 527428 q^{95} - 575396 q^{96} - 1038876 q^{97} - 2413264 q^{98} + 1041038 q^{99} + O(q^{100})$$

Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(336))$$

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
336.6.a $$\chi_{336}(1, \cdot)$$ 336.6.a.a 1 1
336.6.a.b 1
336.6.a.c 1
336.6.a.d 1
336.6.a.e 1
336.6.a.f 1
336.6.a.g 1
336.6.a.h 1
336.6.a.i 1
336.6.a.j 1
336.6.a.k 1
336.6.a.l 1
336.6.a.m 1
336.6.a.n 1
336.6.a.o 1
336.6.a.p 1
336.6.a.q 1
336.6.a.r 1
336.6.a.s 2
336.6.a.t 2
336.6.a.u 2
336.6.a.v 2
336.6.a.w 2
336.6.a.x 2
336.6.b $$\chi_{336}(223, \cdot)$$ 336.6.b.a 6 1
336.6.b.b 6
336.6.b.c 14
336.6.b.d 14
336.6.c $$\chi_{336}(169, \cdot)$$ None 0 1
336.6.h $$\chi_{336}(239, \cdot)$$ 336.6.h.a 20 1
336.6.h.b 40
336.6.i $$\chi_{336}(41, \cdot)$$ None 0 1
336.6.j $$\chi_{336}(71, \cdot)$$ None 0 1
336.6.k $$\chi_{336}(209, \cdot)$$ 336.6.k.a 2 1
336.6.k.b 4
336.6.k.c 8
336.6.k.d 12
336.6.k.e 12
336.6.k.f 40
336.6.p $$\chi_{336}(55, \cdot)$$ None 0 1
336.6.q $$\chi_{336}(193, \cdot)$$ 336.6.q.a 2 2
336.6.q.b 2
336.6.q.c 2
336.6.q.d 2
336.6.q.e 4
336.6.q.f 4
336.6.q.g 4
336.6.q.h 4
336.6.q.i 8
336.6.q.j 8
336.6.q.k 8
336.6.q.l 10
336.6.q.m 10
336.6.q.n 12
336.6.s $$\chi_{336}(155, \cdot)$$ n/a 480 2
336.6.u $$\chi_{336}(139, \cdot)$$ n/a 320 2
336.6.w $$\chi_{336}(85, \cdot)$$ n/a 240 2
336.6.y $$\chi_{336}(125, \cdot)$$ n/a 632 2
336.6.bb $$\chi_{336}(103, \cdot)$$ None 0 2
336.6.bc $$\chi_{336}(17, \cdot)$$ n/a 156 2
336.6.bd $$\chi_{336}(23, \cdot)$$ None 0 2
336.6.bi $$\chi_{336}(89, \cdot)$$ None 0 2
336.6.bj $$\chi_{336}(95, \cdot)$$ n/a 160 2
336.6.bk $$\chi_{336}(25, \cdot)$$ None 0 2
336.6.bl $$\chi_{336}(31, \cdot)$$ 336.6.bl.a 2 2
336.6.bl.b 2
336.6.bl.c 10
336.6.bl.d 10
336.6.bl.e 14
336.6.bl.f 14
336.6.bl.g 14
336.6.bl.h 14
336.6.bo $$\chi_{336}(5, \cdot)$$ n/a 1264 4
336.6.bq $$\chi_{336}(37, \cdot)$$ n/a 640 4
336.6.bs $$\chi_{336}(19, \cdot)$$ n/a 640 4
336.6.bu $$\chi_{336}(11, \cdot)$$ n/a 1264 4

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

Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(336))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(336)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 10}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 10}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 5}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 1}$$