Properties

Label 336.7
Level 336
Weight 7
Dimension 7408
Nonzero newspaces 16
Sturm bound 43008
Trace bound 9

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Defining parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(43008\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(336))\).

Total New Old
Modular forms 18768 7496 11272
Cusp forms 18096 7408 10688
Eisenstein series 672 88 584

Trace form

\( 7408 q - 7 q^{3} + 344 q^{4} - 264 q^{5} - 1028 q^{6} + 340 q^{7} + 3864 q^{8} + 3835 q^{9} + O(q^{10}) \) \( 7408 q - 7 q^{3} + 344 q^{4} - 264 q^{5} - 1028 q^{6} + 340 q^{7} + 3864 q^{8} + 3835 q^{9} - 4504 q^{10} + 5440 q^{11} - 4700 q^{12} - 10032 q^{13} + 15388 q^{14} + 54 q^{15} - 28216 q^{16} + 14664 q^{17} - 29772 q^{18} - 494 q^{19} + 28000 q^{20} + 26723 q^{21} + 166496 q^{22} - 105904 q^{23} - 169700 q^{24} - 58288 q^{25} + 10600 q^{26} + 94700 q^{27} + 69096 q^{28} - 143960 q^{29} + 321756 q^{30} + 153642 q^{31} + 105920 q^{32} - 26195 q^{33} - 501288 q^{34} - 504768 q^{35} - 409016 q^{36} - 294234 q^{37} - 33936 q^{38} + 300646 q^{39} + 946904 q^{40} + 259848 q^{41} + 569960 q^{42} - 183248 q^{43} - 508048 q^{44} - 674607 q^{45} - 1555520 q^{46} - 376992 q^{47} - 302468 q^{48} - 3892592 q^{49} + 1549472 q^{50} - 515425 q^{51} + 2088272 q^{52} + 730648 q^{53} + 972244 q^{54} - 844404 q^{55} - 1122632 q^{56} - 1478306 q^{57} - 1119616 q^{58} + 443072 q^{59} - 3785796 q^{60} + 641142 q^{61} - 1253568 q^{62} + 17181 q^{63} + 3740648 q^{64} + 2599280 q^{65} + 3060532 q^{66} + 2026210 q^{67} - 880664 q^{68} - 346842 q^{69} - 4337232 q^{70} - 2595392 q^{71} - 1504020 q^{72} + 67798 q^{73} + 9789672 q^{74} - 747210 q^{75} + 7045064 q^{76} + 860672 q^{77} - 2281960 q^{78} - 3515094 q^{79} - 9336144 q^{80} + 7169739 q^{81} - 5329544 q^{82} + 4995520 q^{83} - 581572 q^{84} - 2522700 q^{85} - 8285856 q^{86} - 75996 q^{87} + 3069800 q^{88} + 7030824 q^{89} + 1598340 q^{90} + 2383688 q^{91} + 8515544 q^{92} + 6718613 q^{93} + 9584904 q^{94} - 13446720 q^{95} + 6957788 q^{96} - 1291120 q^{97} + 6674416 q^{98} + 1425958 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(336))\)

We only show spaces with odd 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
336.7.d \(\chi_{336}(113, \cdot)\) 336.7.d.a 12 1
336.7.d.b 12
336.7.d.c 12
336.7.d.d 36
336.7.e \(\chi_{336}(167, \cdot)\) None 0 1
336.7.f \(\chi_{336}(97, \cdot)\) 336.7.f.a 8 1
336.7.f.b 8
336.7.f.c 8
336.7.f.d 24
336.7.g \(\chi_{336}(295, \cdot)\) None 0 1
336.7.l \(\chi_{336}(265, \cdot)\) None 0 1
336.7.m \(\chi_{336}(127, \cdot)\) 336.7.m.a 12 1
336.7.m.b 12
336.7.m.c 12
336.7.n \(\chi_{336}(281, \cdot)\) None 0 1
336.7.o \(\chi_{336}(335, \cdot)\) 336.7.o.a 2 1
336.7.o.b 2
336.7.o.c 2
336.7.o.d 2
336.7.o.e 24
336.7.o.f 64
336.7.r \(\chi_{336}(13, \cdot)\) n/a 384 2
336.7.t \(\chi_{336}(29, \cdot)\) n/a 576 2
336.7.v \(\chi_{336}(83, \cdot)\) n/a 760 2
336.7.x \(\chi_{336}(43, \cdot)\) n/a 288 2
336.7.z \(\chi_{336}(47, \cdot)\) n/a 192 2
336.7.ba \(\chi_{336}(137, \cdot)\) None 0 2
336.7.be \(\chi_{336}(79, \cdot)\) 336.7.be.a 16 2
336.7.be.b 16
336.7.be.c 16
336.7.be.d 16
336.7.be.e 16
336.7.be.f 16
336.7.bf \(\chi_{336}(73, \cdot)\) None 0 2
336.7.bg \(\chi_{336}(151, \cdot)\) None 0 2
336.7.bh \(\chi_{336}(145, \cdot)\) 336.7.bh.a 8 2
336.7.bh.b 8
336.7.bh.c 8
336.7.bh.d 8
336.7.bh.e 8
336.7.bh.f 8
336.7.bh.g 24
336.7.bh.h 24
336.7.bm \(\chi_{336}(215, \cdot)\) None 0 2
336.7.bn \(\chi_{336}(65, \cdot)\) n/a 188 2
336.7.bp \(\chi_{336}(67, \cdot)\) n/a 768 4
336.7.br \(\chi_{336}(59, \cdot)\) n/a 1520 4
336.7.bt \(\chi_{336}(53, \cdot)\) n/a 1520 4
336.7.bv \(\chi_{336}(61, \cdot)\) n/a 768 4

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(336))\) into lower level spaces

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