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Properties

Label 483.4
Level 483
Weight 4
Dimension 17936
Nonzero newspaces 16
Sturm bound 67584
Trace bound 3

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Defining parameters

Level: \( N \) = \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(67584\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(483))\).

Total New Old
Modular forms 25872 18352 7520
Cusp forms 24816 17936 6880
Eisenstein series 1056 416 640

Trace form

\( 17936 q - 50 q^{3} - 76 q^{4} + 48 q^{5} + 28 q^{6} - 2 q^{7} - 108 q^{8} - 122 q^{9} + O(q^{10}) \) \( 17936 q - 50 q^{3} - 76 q^{4} + 48 q^{5} + 28 q^{6} - 2 q^{7} - 108 q^{8} - 122 q^{9} - 184 q^{10} + 148 q^{12} + 80 q^{13} + 624 q^{14} - 462 q^{15} - 1596 q^{16} - 328 q^{17} - 408 q^{18} - 764 q^{19} + 728 q^{20} - 565 q^{21} + 808 q^{22} + 2104 q^{23} + 2264 q^{24} + 2172 q^{25} + 1468 q^{26} + 304 q^{27} + 1406 q^{28} + 416 q^{29} + 24 q^{30} - 788 q^{31} - 3548 q^{32} - 378 q^{33} - 7192 q^{34} - 3028 q^{35} - 2606 q^{36} - 7684 q^{37} - 5840 q^{38} - 2204 q^{39} + 2360 q^{40} + 1816 q^{41} - 1069 q^{42} + 4340 q^{43} + 8876 q^{44} - 4368 q^{45} + 15044 q^{46} + 5984 q^{47} + 8756 q^{48} + 8938 q^{49} + 14216 q^{50} + 7414 q^{51} + 10592 q^{52} + 3232 q^{53} + 13332 q^{54} - 5968 q^{55} - 8530 q^{56} - 3242 q^{57} - 31564 q^{58} - 11384 q^{59} - 12544 q^{60} - 6364 q^{61} - 3624 q^{62} - 6711 q^{63} - 8776 q^{64} - 1008 q^{65} - 13314 q^{66} - 1924 q^{67} + 3072 q^{68} - 5868 q^{69} + 6788 q^{70} + 984 q^{71} - 6728 q^{72} + 8564 q^{73} - 4000 q^{74} - 15368 q^{75} - 21780 q^{76} - 10112 q^{77} - 18234 q^{78} - 10508 q^{79} - 22428 q^{80} - 5290 q^{81} - 14800 q^{82} - 5056 q^{83} + 775 q^{84} + 12004 q^{85} + 16508 q^{86} + 15388 q^{87} + 28528 q^{88} + 25944 q^{89} + 39494 q^{90} + 14276 q^{91} + 40740 q^{92} + 24674 q^{93} + 32212 q^{94} + 13416 q^{95} + 16378 q^{96} - 9928 q^{97} - 862 q^{98} + 12478 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(483))\)

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
483.4.a \(\chi_{483}(1, \cdot)\) 483.4.a.a 3 1
483.4.a.b 4
483.4.a.c 7
483.4.a.d 7
483.4.a.e 7
483.4.a.f 9
483.4.a.g 9
483.4.a.h 9
483.4.a.i 9
483.4.d \(\chi_{483}(461, \cdot)\) n/a 176 1
483.4.e \(\chi_{483}(344, \cdot)\) n/a 144 1
483.4.h \(\chi_{483}(160, \cdot)\) 483.4.h.a 96 1
483.4.i \(\chi_{483}(277, \cdot)\) n/a 176 2
483.4.j \(\chi_{483}(229, \cdot)\) n/a 192 2
483.4.m \(\chi_{483}(137, \cdot)\) n/a 376 2
483.4.n \(\chi_{483}(47, \cdot)\) n/a 352 2
483.4.q \(\chi_{483}(64, \cdot)\) n/a 720 10
483.4.r \(\chi_{483}(34, \cdot)\) n/a 960 10
483.4.u \(\chi_{483}(113, \cdot)\) n/a 1440 10
483.4.v \(\chi_{483}(41, \cdot)\) n/a 1880 10
483.4.y \(\chi_{483}(4, \cdot)\) n/a 1920 20
483.4.bb \(\chi_{483}(26, \cdot)\) n/a 3760 20
483.4.bc \(\chi_{483}(11, \cdot)\) n/a 3760 20
483.4.bf \(\chi_{483}(10, \cdot)\) n/a 1920 20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(483))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(483)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)