Properties

Label 833.4
Level 833
Weight 4
Dimension 79960
Nonzero newspaces 20
Sturm bound 225792
Trace bound 2

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Defining parameters

Level: \( N \) = \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(225792\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(833))\).

Total New Old
Modular forms 85632 81414 4218
Cusp forms 83712 79960 3752
Eisenstein series 1920 1454 466

Trace form

\( 79960 q - 218 q^{2} - 242 q^{3} - 218 q^{4} - 170 q^{5} - 86 q^{6} - 204 q^{7} - 494 q^{8} - 386 q^{9} + O(q^{10}) \) \( 79960 q - 218 q^{2} - 242 q^{3} - 218 q^{4} - 170 q^{5} - 86 q^{6} - 204 q^{7} - 494 q^{8} - 386 q^{9} - 430 q^{10} - 330 q^{11} - 134 q^{12} - 174 q^{13} - 204 q^{14} + 238 q^{15} + 462 q^{16} + 51 q^{17} - 90 q^{18} - 762 q^{19} - 766 q^{20} - 708 q^{21} - 634 q^{22} + 414 q^{23} - 1526 q^{24} - 606 q^{25} - 1238 q^{26} - 302 q^{27} + 132 q^{28} - 78 q^{29} + 874 q^{30} + 118 q^{31} - 314 q^{32} + 1046 q^{33} + 1609 q^{34} - 660 q^{35} + 5130 q^{36} + 3310 q^{37} + 4722 q^{38} + 2862 q^{39} + 4978 q^{40} + 2574 q^{41} - 498 q^{42} - 3818 q^{43} - 9070 q^{44} - 11194 q^{45} - 10718 q^{46} - 3354 q^{47} - 12868 q^{48} - 8016 q^{49} - 7332 q^{50} - 2077 q^{51} - 9478 q^{52} - 4726 q^{53} - 7550 q^{54} - 4146 q^{55} + 216 q^{56} + 3190 q^{57} + 5346 q^{58} + 7798 q^{59} + 21226 q^{60} + 10318 q^{61} + 11490 q^{62} + 9456 q^{63} + 9674 q^{64} + 3078 q^{65} + 5186 q^{66} + 1246 q^{67} + 2489 q^{68} - 5998 q^{69} - 1002 q^{70} - 6698 q^{71} + 582 q^{72} + 1738 q^{73} - 710 q^{74} + 1738 q^{75} + 1794 q^{76} + 216 q^{77} + 4286 q^{78} + 1614 q^{79} + 28336 q^{80} + 31250 q^{81} + 25880 q^{82} + 16810 q^{83} + 38436 q^{84} + 1387 q^{85} + 1820 q^{86} + 1930 q^{87} - 2672 q^{88} - 1274 q^{89} - 30036 q^{90} - 10662 q^{91} - 12844 q^{92} - 40986 q^{93} - 33896 q^{94} - 35306 q^{95} - 44164 q^{96} - 22052 q^{97} - 55224 q^{98} + 14976 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(833))\)

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
833.4.a \(\chi_{833}(1, \cdot)\) 833.4.a.a 1 1
833.4.a.b 1
833.4.a.c 3
833.4.a.d 3
833.4.a.e 4
833.4.a.f 7
833.4.a.g 9
833.4.a.h 12
833.4.a.i 12
833.4.a.j 14
833.4.a.k 14
833.4.a.l 18
833.4.a.m 18
833.4.a.n 24
833.4.a.o 24
833.4.b \(\chi_{833}(50, \cdot)\) n/a 180 1
833.4.e \(\chi_{833}(18, \cdot)\) n/a 320 2
833.4.g \(\chi_{833}(344, \cdot)\) n/a 360 2
833.4.j \(\chi_{833}(67, \cdot)\) n/a 352 2
833.4.k \(\chi_{833}(120, \cdot)\) n/a 1344 6
833.4.l \(\chi_{833}(246, \cdot)\) n/a 716 4
833.4.o \(\chi_{833}(30, \cdot)\) n/a 704 4
833.4.r \(\chi_{833}(169, \cdot)\) n/a 1500 6
833.4.t \(\chi_{833}(48, \cdot)\) n/a 1408 8
833.4.u \(\chi_{833}(86, \cdot)\) n/a 2688 12
833.4.v \(\chi_{833}(128, \cdot)\) n/a 1408 8
833.4.x \(\chi_{833}(64, \cdot)\) n/a 3000 12
833.4.z \(\chi_{833}(16, \cdot)\) n/a 3000 12
833.4.bc \(\chi_{833}(31, \cdot)\) n/a 2816 16
833.4.bf \(\chi_{833}(8, \cdot)\) n/a 6000 24
833.4.bg \(\chi_{833}(4, \cdot)\) n/a 6000 24
833.4.bi \(\chi_{833}(6, \cdot)\) n/a 12000 48
833.4.bl \(\chi_{833}(2, \cdot)\) n/a 12000 48
833.4.bn \(\chi_{833}(3, \cdot)\) n/a 24000 96

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(833))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(833)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)