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Properties

Label 464.6
Level 464
Weight 6
Dimension 18734
Nonzero newspaces 14
Sturm bound 80640
Trace bound 3

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Defining parameters

Level: \( N \) = \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(80640\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(464))\).

Total New Old
Modular forms 33992 18976 15016
Cusp forms 33208 18734 14474
Eisenstein series 784 242 542

Trace form

\( 18734 q - 52 q^{2} - 22 q^{3} - 8 q^{4} - 26 q^{5} - 280 q^{6} - 266 q^{7} - 544 q^{8} - 130 q^{9} + O(q^{10}) \) \( 18734 q - 52 q^{2} - 22 q^{3} - 8 q^{4} - 26 q^{5} - 280 q^{6} - 266 q^{7} - 544 q^{8} - 130 q^{9} + 816 q^{10} + 2498 q^{11} - 64 q^{12} - 186 q^{13} + 144 q^{14} - 7890 q^{15} + 1688 q^{16} + 1090 q^{17} + 6220 q^{18} + 12442 q^{19} - 6000 q^{20} - 2190 q^{21} - 8896 q^{22} - 7882 q^{23} - 16792 q^{24} - 4298 q^{25} - 14792 q^{26} - 3706 q^{27} + 14616 q^{28} - 264 q^{29} + 60776 q^{30} + 20086 q^{31} + 47928 q^{32} + 7882 q^{33} + 3424 q^{34} - 23266 q^{35} - 13840 q^{36} + 1174 q^{37} - 106552 q^{38} + 29110 q^{39} - 150600 q^{40} - 16694 q^{41} - 66856 q^{42} - 11854 q^{43} + 80192 q^{44} + 22334 q^{45} + 185008 q^{46} - 43658 q^{47} + 295928 q^{48} + 79282 q^{49} + 170044 q^{50} - 56722 q^{51} - 183200 q^{52} - 111882 q^{53} - 417400 q^{54} + 39926 q^{55} - 382312 q^{56} - 101724 q^{57} - 106832 q^{58} + 77800 q^{59} + 308680 q^{60} + 202534 q^{61} + 547688 q^{62} + 34158 q^{63} + 567496 q^{64} + 60394 q^{65} + 306656 q^{66} + 162938 q^{67} - 267480 q^{68} - 151534 q^{69} - 824376 q^{70} - 157706 q^{71} - 940544 q^{72} - 125366 q^{73} - 294352 q^{74} - 210438 q^{75} + 174880 q^{76} + 18802 q^{77} + 1263504 q^{78} + 40982 q^{79} + 1108856 q^{80} + 221610 q^{81} + 186376 q^{82} - 185558 q^{83} - 381832 q^{84} + 35778 q^{85} - 940992 q^{86} - 58554 q^{87} - 1180768 q^{88} - 203510 q^{89} - 560360 q^{90} + 512910 q^{91} + 443736 q^{92} - 30182 q^{93} + 921768 q^{94} + 140494 q^{95} + 1194600 q^{96} - 978710 q^{97} + 889236 q^{98} + 642274 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(464))\)

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
464.6.a \(\chi_{464}(1, \cdot)\) 464.6.a.a 1 1
464.6.a.b 1
464.6.a.c 2
464.6.a.d 2
464.6.a.e 2
464.6.a.f 3
464.6.a.g 4
464.6.a.h 4
464.6.a.i 4
464.6.a.j 6
464.6.a.k 7
464.6.a.l 8
464.6.a.m 8
464.6.a.n 9
464.6.a.o 9
464.6.c \(\chi_{464}(233, \cdot)\) None 0 1
464.6.e \(\chi_{464}(289, \cdot)\) 464.6.e.a 12 1
464.6.e.b 12
464.6.e.c 12
464.6.e.d 38
464.6.g \(\chi_{464}(57, \cdot)\) None 0 1
464.6.j \(\chi_{464}(307, \cdot)\) n/a 596 2
464.6.k \(\chi_{464}(191, \cdot)\) n/a 150 2
464.6.m \(\chi_{464}(173, \cdot)\) n/a 596 2
464.6.n \(\chi_{464}(117, \cdot)\) n/a 560 2
464.6.q \(\chi_{464}(215, \cdot)\) None 0 2
464.6.t \(\chi_{464}(75, \cdot)\) n/a 596 2
464.6.u \(\chi_{464}(49, \cdot)\) n/a 444 6
464.6.w \(\chi_{464}(9, \cdot)\) None 0 6
464.6.y \(\chi_{464}(33, \cdot)\) n/a 444 6
464.6.ba \(\chi_{464}(25, \cdot)\) None 0 6
464.6.bc \(\chi_{464}(11, \cdot)\) n/a 3576 12
464.6.bf \(\chi_{464}(39, \cdot)\) None 0 12
464.6.bi \(\chi_{464}(45, \cdot)\) n/a 3576 12
464.6.bj \(\chi_{464}(5, \cdot)\) n/a 3576 12
464.6.bl \(\chi_{464}(15, \cdot)\) n/a 900 12
464.6.bm \(\chi_{464}(3, \cdot)\) n/a 3576 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(464))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(464)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 2}\)