Properties

Label 462.6
Level 462
Weight 6
Dimension 6784
Nonzero newspaces 16
Sturm bound 69120
Trace bound 4

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Defining parameters

Level: \( N \) = \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(69120\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(462))\).

Total New Old
Modular forms 29280 6784 22496
Cusp forms 28320 6784 21536
Eisenstein series 960 0 960

Trace form

\( 6784 q + 16 q^{2} - 64 q^{4} + 328 q^{6} + 100 q^{7} + 256 q^{8} + 1060 q^{9} + O(q^{10}) \) \( 6784 q + 16 q^{2} - 64 q^{4} + 328 q^{6} + 100 q^{7} + 256 q^{8} + 1060 q^{9} - 32 q^{10} + 2552 q^{11} + 320 q^{12} + 2656 q^{13} - 2992 q^{14} - 2540 q^{15} + 1024 q^{16} - 11360 q^{17} + 7960 q^{18} + 9756 q^{19} - 4224 q^{20} - 4056 q^{21} - 480 q^{22} + 5504 q^{23} + 896 q^{24} + 14252 q^{25} - 15808 q^{26} + 40260 q^{27} - 17024 q^{28} - 36976 q^{29} - 56880 q^{30} + 53240 q^{31} + 4096 q^{32} - 49662 q^{33} + 48864 q^{34} - 4076 q^{35} - 23776 q^{36} + 83320 q^{37} + 10400 q^{38} + 25900 q^{39} - 64512 q^{40} - 61744 q^{41} - 67160 q^{42} + 15720 q^{43} - 66688 q^{44} - 136992 q^{45} - 14720 q^{46} - 80344 q^{47} - 70732 q^{49} + 232112 q^{50} + 90774 q^{51} + 198784 q^{52} + 219624 q^{53} + 167472 q^{54} + 511116 q^{55} - 61952 q^{56} + 317834 q^{57} - 30976 q^{58} - 293592 q^{59} - 148608 q^{60} - 1899144 q^{61} - 560320 q^{62} - 551170 q^{63} + 180224 q^{64} + 372096 q^{65} + 573248 q^{66} + 755128 q^{67} + 338560 q^{68} + 1019168 q^{69} + 871552 q^{70} + 149936 q^{71} - 90368 q^{72} + 227192 q^{73} - 310656 q^{74} - 273198 q^{75} - 266240 q^{76} - 1993604 q^{77} - 929824 q^{78} - 2380960 q^{79} - 225280 q^{80} - 1268548 q^{81} - 629008 q^{82} - 82320 q^{83} + 385728 q^{84} + 2753336 q^{85} + 1794080 q^{86} + 1661172 q^{87} + 640768 q^{88} + 1603056 q^{89} + 1641904 q^{90} + 1983104 q^{91} + 392448 q^{92} + 929312 q^{93} - 1571744 q^{94} - 1966824 q^{95} + 24576 q^{96} - 2397204 q^{97} - 266672 q^{98} - 1847076 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(462))\)

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
462.6.a \(\chi_{462}(1, \cdot)\) 462.6.a.a 1 1
462.6.a.b 1
462.6.a.c 1
462.6.a.d 1
462.6.a.e 2
462.6.a.f 2
462.6.a.g 2
462.6.a.h 2
462.6.a.i 2
462.6.a.j 2
462.6.a.k 2
462.6.a.l 2
462.6.a.m 3
462.6.a.n 3
462.6.a.o 3
462.6.a.p 3
462.6.a.q 4
462.6.a.r 4
462.6.a.s 4
462.6.a.t 4
462.6.c \(\chi_{462}(197, \cdot)\) n/a 120 1
462.6.e \(\chi_{462}(307, \cdot)\) 462.6.e.a 40 1
462.6.e.b 40
462.6.g \(\chi_{462}(419, \cdot)\) n/a 136 1
462.6.i \(\chi_{462}(67, \cdot)\) n/a 136 2
462.6.j \(\chi_{462}(169, \cdot)\) n/a 240 4
462.6.k \(\chi_{462}(89, \cdot)\) n/a 264 2
462.6.n \(\chi_{462}(65, \cdot)\) n/a 320 2
462.6.p \(\chi_{462}(241, \cdot)\) n/a 160 2
462.6.s \(\chi_{462}(125, \cdot)\) n/a 640 4
462.6.u \(\chi_{462}(13, \cdot)\) n/a 320 4
462.6.w \(\chi_{462}(29, \cdot)\) n/a 480 4
462.6.y \(\chi_{462}(25, \cdot)\) n/a 640 8
462.6.ba \(\chi_{462}(19, \cdot)\) n/a 640 8
462.6.bc \(\chi_{462}(95, \cdot)\) n/a 1280 8
462.6.bf \(\chi_{462}(5, \cdot)\) n/a 1280 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(462))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(462)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)