↑

Properties

Label 1083.4
Level 1083
Weight 4
Dimension 96462
Nonzero newspaces 12
Sturm bound 346560
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1083 = 3 \cdot 19^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(346560\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1083))\).

Total New Old
Modular forms 130968 97398 33570
Cusp forms 128952 96462 32490
Eisenstein series 2016 936 1080

Trace form

\( 96462 q - 153 q^{3} - 306 q^{4} - 153 q^{6} - 306 q^{7} - 153 q^{9} + O(q^{10}) \) \( 96462 q - 153 q^{3} - 306 q^{4} - 153 q^{6} - 306 q^{7} - 153 q^{9} - 306 q^{10} - 729 q^{12} - 882 q^{13} - 144 q^{14} + 63 q^{15} + 1422 q^{16} + 576 q^{17} - 171 q^{18} + 432 q^{19} + 2304 q^{20} + 351 q^{21} + 342 q^{22} - 72 q^{23} - 1017 q^{24} - 2034 q^{25} - 2736 q^{26} - 1791 q^{27} - 9486 q^{28} - 2520 q^{29} - 2547 q^{30} - 666 q^{31} + 1260 q^{32} + 1683 q^{33} + 4194 q^{34} + 4464 q^{35} + 6291 q^{36} + 2322 q^{37} + 4662 q^{38} + 3483 q^{39} + 7218 q^{40} + 1800 q^{41} + 2907 q^{42} + 702 q^{43} - 900 q^{44} + 1899 q^{45} - 6606 q^{46} - 3816 q^{47} - 7335 q^{48} - 7146 q^{49} - 12852 q^{50} - 5103 q^{51} - 306 q^{52} - 5553 q^{54} - 306 q^{55} - 2682 q^{57} - 594 q^{58} - 16083 q^{60} - 16506 q^{61} - 19260 q^{62} - 3105 q^{63} - 16722 q^{64} - 7560 q^{65} + 2583 q^{66} + 558 q^{67} + 4788 q^{68} + 9999 q^{69} + 19134 q^{70} + 7920 q^{71} + 15435 q^{72} + 22050 q^{73} + 21024 q^{74} + 12429 q^{75} + 13176 q^{76} + 18648 q^{77} - 693 q^{78} + 10350 q^{79} - 9216 q^{80} - 6489 q^{81} + 8586 q^{82} - 1368 q^{83} - 2961 q^{84} - 4050 q^{85} - 5652 q^{86} - 2889 q^{87} - 4914 q^{88} - 16200 q^{89} + 10557 q^{90} - 20178 q^{91} - 10116 q^{92} - 765 q^{93} + 7506 q^{94} + 5076 q^{95} + 53991 q^{96} + 9198 q^{97} + 23616 q^{98} + 22725 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1083))\)

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
1083.4.a \(\chi_{1083}(1, \cdot)\) 1083.4.a.a 1 1
1083.4.a.b 2
1083.4.a.c 3
1083.4.a.d 4
1083.4.a.e 4
1083.4.a.f 4
1083.4.a.g 5
1083.4.a.h 5
1083.4.a.i 5
1083.4.a.j 5
1083.4.a.k 10
1083.4.a.l 10
1083.4.a.m 10
1083.4.a.n 10
1083.4.a.o 12
1083.4.a.p 12
1083.4.a.q 16
1083.4.a.r 16
1083.4.a.s 18
1083.4.a.t 18
1083.4.d \(\chi_{1083}(1082, \cdot)\) n/a 324 1
1083.4.e \(\chi_{1083}(292, \cdot)\) n/a 340 2
1083.4.f \(\chi_{1083}(293, \cdot)\) n/a 648 2
1083.4.i \(\chi_{1083}(28, \cdot)\) n/a 1020 6
1083.4.j \(\chi_{1083}(116, \cdot)\) n/a 1944 6
1083.4.m \(\chi_{1083}(58, \cdot)\) n/a 3420 18
1083.4.n \(\chi_{1083}(56, \cdot)\) n/a 6804 18
1083.4.q \(\chi_{1083}(7, \cdot)\) n/a 6840 36
1083.4.t \(\chi_{1083}(8, \cdot)\) n/a 13608 36
1083.4.u \(\chi_{1083}(4, \cdot)\) n/a 20520 108
1083.4.x \(\chi_{1083}(2, \cdot)\) n/a 40824 108

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1083))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1083)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)