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Properties

Label 800.3
Level 800
Weight 3
Dimension 19703
Nonzero newspaces 20
Sturm bound 115200
Trace bound 7

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Defining parameters

Level: \( N \) = \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(115200\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(800))\).

Total New Old
Modular forms 39296 20113 19183
Cusp forms 37504 19703 17801
Eisenstein series 1792 410 1382

Trace form

\( 19703 q - 52 q^{2} - 38 q^{3} - 52 q^{4} - 64 q^{5} - 84 q^{6} - 40 q^{7} - 52 q^{8} - 95 q^{9} + O(q^{10}) \) \( 19703 q - 52 q^{2} - 38 q^{3} - 52 q^{4} - 64 q^{5} - 84 q^{6} - 40 q^{7} - 52 q^{8} - 95 q^{9} - 64 q^{10} - 78 q^{11} - 100 q^{12} - 80 q^{13} - 68 q^{14} - 48 q^{15} - 64 q^{16} + 14 q^{17} + 8 q^{18} - 14 q^{19} - 64 q^{20} - 20 q^{21} + 96 q^{22} - 104 q^{23} + 160 q^{24} - 96 q^{25} - 64 q^{26} - 236 q^{27} + 8 q^{28} - 240 q^{29} - 64 q^{30} - 316 q^{31} - 72 q^{32} - 508 q^{33} - 96 q^{34} - 144 q^{35} - 416 q^{36} - 272 q^{37} - 444 q^{38} + 160 q^{39} - 64 q^{40} - 70 q^{41} - 472 q^{42} + 298 q^{43} - 236 q^{44} + 176 q^{45} - 116 q^{46} + 340 q^{47} + 635 q^{49} - 64 q^{50} + 492 q^{51} + 372 q^{52} + 144 q^{53} + 544 q^{54} + 52 q^{55} + 472 q^{56} + 232 q^{57} + 480 q^{58} + 162 q^{59} + 192 q^{60} + 16 q^{61} + 168 q^{62} + 428 q^{63} + 1160 q^{64} + 288 q^{65} + 2668 q^{66} + 314 q^{67} + 2048 q^{68} + 1740 q^{69} + 1232 q^{70} + 192 q^{71} + 2564 q^{72} + 682 q^{73} + 1180 q^{74} + 176 q^{75} + 92 q^{76} + 492 q^{77} + 324 q^{78} - 516 q^{79} - 224 q^{80} - 753 q^{81} - 372 q^{82} - 998 q^{83} - 2096 q^{84} - 640 q^{85} - 1184 q^{86} - 1456 q^{87} - 2544 q^{88} - 1270 q^{89} - 2704 q^{90} - 1024 q^{91} - 3176 q^{92} - 2448 q^{93} - 3368 q^{94} - 532 q^{95} - 4560 q^{96} - 1402 q^{97} - 2200 q^{98} - 1034 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(800))\)

We only show spaces with odd 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
800.3.b \(\chi_{800}(351, \cdot)\) 800.3.b.a 2 1
800.3.b.b 4
800.3.b.c 4
800.3.b.d 4
800.3.b.e 4
800.3.b.f 4
800.3.b.g 4
800.3.b.h 6
800.3.b.i 6
800.3.e \(\chi_{800}(399, \cdot)\) 800.3.e.a 2 1
800.3.e.b 4
800.3.e.c 12
800.3.e.d 16
800.3.g \(\chi_{800}(751, \cdot)\) 800.3.g.a 1 1
800.3.g.b 2
800.3.g.c 2
800.3.g.d 2
800.3.g.e 6
800.3.g.f 6
800.3.g.g 8
800.3.g.h 8
800.3.h \(\chi_{800}(799, \cdot)\) 800.3.h.a 2 1
800.3.h.b 2
800.3.h.c 4
800.3.h.d 4
800.3.h.e 4
800.3.h.f 4
800.3.h.g 4
800.3.h.h 4
800.3.h.i 4
800.3.h.j 4
800.3.i \(\chi_{800}(57, \cdot)\) None 0 2
800.3.k \(\chi_{800}(199, \cdot)\) None 0 2
800.3.m \(\chi_{800}(593, \cdot)\) 800.3.m.a 16 2
800.3.m.b 20
800.3.m.c 32
800.3.p \(\chi_{800}(193, \cdot)\) 800.3.p.a 2 2
800.3.p.b 2
800.3.p.c 4
800.3.p.d 4
800.3.p.e 4
800.3.p.f 4
800.3.p.g 4
800.3.p.h 4
800.3.p.i 6
800.3.p.j 6
800.3.p.k 8
800.3.p.l 8
800.3.p.m 8
800.3.p.n 8
800.3.r \(\chi_{800}(151, \cdot)\) None 0 2
800.3.t \(\chi_{800}(457, \cdot)\) None 0 2
800.3.w \(\chi_{800}(93, \cdot)\) n/a 568 4
800.3.x \(\chi_{800}(51, \cdot)\) n/a 596 4
800.3.z \(\chi_{800}(99, \cdot)\) n/a 568 4
800.3.bc \(\chi_{800}(157, \cdot)\) n/a 568 4
800.3.bd \(\chi_{800}(111, \cdot)\) n/a 232 4
800.3.bf \(\chi_{800}(159, \cdot)\) n/a 240 4
800.3.bh \(\chi_{800}(31, \cdot)\) n/a 240 4
800.3.bi \(\chi_{800}(79, \cdot)\) n/a 232 4
800.3.bk \(\chi_{800}(137, \cdot)\) None 0 8
800.3.bn \(\chi_{800}(39, \cdot)\) None 0 8
800.3.bo \(\chi_{800}(33, \cdot)\) n/a 480 8
800.3.br \(\chi_{800}(17, \cdot)\) n/a 464 8
800.3.bs \(\chi_{800}(71, \cdot)\) None 0 8
800.3.bv \(\chi_{800}(73, \cdot)\) None 0 8
800.3.bw \(\chi_{800}(13, \cdot)\) n/a 3808 16
800.3.bz \(\chi_{800}(19, \cdot)\) n/a 3808 16
800.3.cb \(\chi_{800}(11, \cdot)\) n/a 3808 16
800.3.cc \(\chi_{800}(53, \cdot)\) n/a 3808 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(800))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(800)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)