Properties

Label 464.4
Level 464
Weight 4
Dimension 11192
Nonzero newspaces 14
Sturm bound 53760
Trace bound 3

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Defining parameters

Level: \( N \) = \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(53760\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(464))\).

Total New Old
Modular forms 20552 11434 9118
Cusp forms 19768 11192 8576
Eisenstein series 784 242 542

Trace form

\( 11192 q - 52 q^{2} - 46 q^{3} - 72 q^{4} - 62 q^{5} + 8 q^{6} + 6 q^{7} + 32 q^{8} + 8 q^{9} + O(q^{10}) \) \( 11192 q - 52 q^{2} - 46 q^{3} - 72 q^{4} - 62 q^{5} + 8 q^{6} + 6 q^{7} + 32 q^{8} + 8 q^{9} + 80 q^{10} - 166 q^{11} - 256 q^{12} - 110 q^{13} - 432 q^{14} + 222 q^{15} - 616 q^{16} - 218 q^{17} - 404 q^{18} + 98 q^{19} + 336 q^{20} + 18 q^{21} + 1120 q^{22} - 154 q^{23} + 1640 q^{24} + 228 q^{25} + 472 q^{26} - 106 q^{27} - 616 q^{28} - 66 q^{29} - 2584 q^{30} - 1098 q^{31} - 1992 q^{32} - 470 q^{33} - 928 q^{34} - 1090 q^{35} + 1136 q^{36} + 274 q^{37} + 2408 q^{38} - 218 q^{39} + 2616 q^{40} + 382 q^{41} + 1304 q^{42} + 1738 q^{43} - 1792 q^{44} - 502 q^{45} - 2320 q^{46} + 2902 q^{47} - 3592 q^{48} - 780 q^{49} - 1508 q^{50} + 2558 q^{51} + 416 q^{52} + 1170 q^{53} + 2696 q^{54} + 134 q^{55} + 920 q^{56} + 324 q^{57} - 64 q^{58} - 4832 q^{59} + 328 q^{60} - 2990 q^{61} + 104 q^{62} - 5826 q^{63} - 1080 q^{64} + 946 q^{65} + 800 q^{66} - 3550 q^{67} + 1704 q^{68} - 1678 q^{69} - 376 q^{70} + 1414 q^{71} - 2240 q^{72} - 322 q^{73} + 848 q^{74} + 6834 q^{75} + 2400 q^{76} + 2578 q^{77} + 1488 q^{78} + 7478 q^{79} + 5240 q^{80} - 468 q^{81} + 1352 q^{82} + 5554 q^{83} - 3976 q^{84} + 154 q^{85} - 7584 q^{86} - 834 q^{87} - 3168 q^{88} - 1442 q^{89} - 3848 q^{90} - 5650 q^{91} - 1320 q^{92} + 3034 q^{93} + 6440 q^{94} - 14018 q^{95} + 8808 q^{96} - 11874 q^{97} - 684 q^{98} - 35366 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(464))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
464.4.a \(\chi_{464}(1, \cdot)\) 464.4.a.a 1 1
464.4.a.b 1
464.4.a.c 2
464.4.a.d 2
464.4.a.e 2
464.4.a.f 2
464.4.a.g 3
464.4.a.h 3
464.4.a.i 3
464.4.a.j 3
464.4.a.k 4
464.4.a.l 5
464.4.a.m 5
464.4.a.n 6
464.4.c \(\chi_{464}(233, \cdot)\) None 0 1
464.4.e \(\chi_{464}(289, \cdot)\) 464.4.e.a 6 1
464.4.e.b 8
464.4.e.c 8
464.4.e.d 22
464.4.g \(\chi_{464}(57, \cdot)\) None 0 1
464.4.j \(\chi_{464}(307, \cdot)\) n/a 356 2
464.4.k \(\chi_{464}(191, \cdot)\) 464.4.k.a 2 2
464.4.k.b 28
464.4.k.c 60
464.4.m \(\chi_{464}(173, \cdot)\) n/a 356 2
464.4.n \(\chi_{464}(117, \cdot)\) n/a 336 2
464.4.q \(\chi_{464}(215, \cdot)\) None 0 2
464.4.t \(\chi_{464}(75, \cdot)\) n/a 356 2
464.4.u \(\chi_{464}(49, \cdot)\) n/a 264 6
464.4.w \(\chi_{464}(9, \cdot)\) None 0 6
464.4.y \(\chi_{464}(33, \cdot)\) n/a 264 6
464.4.ba \(\chi_{464}(25, \cdot)\) None 0 6
464.4.bc \(\chi_{464}(11, \cdot)\) n/a 2136 12
464.4.bf \(\chi_{464}(39, \cdot)\) None 0 12
464.4.bi \(\chi_{464}(45, \cdot)\) n/a 2136 12
464.4.bj \(\chi_{464}(5, \cdot)\) n/a 2136 12
464.4.bl \(\chi_{464}(15, \cdot)\) n/a 540 12
464.4.bm \(\chi_{464}(3, \cdot)\) n/a 2136 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(464))\) into lower level spaces

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