Properties

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

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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 the 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

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