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Properties

Label 1600.3
Level 1600
Weight 3
Dimension 79181
Nonzero newspaces 28
Sturm bound 460800
Trace bound 12

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Defining parameters

Level: \( N \) = \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(460800\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1600))\).

Total New Old
Modular forms 155616 80083 75533
Cusp forms 151584 79181 72403
Eisenstein series 4032 902 3130

Trace form

\( 79181 q - 104 q^{2} - 78 q^{3} - 104 q^{4} - 128 q^{5} - 168 q^{6} - 76 q^{7} - 104 q^{8} - 121 q^{9} + O(q^{10}) \) \( 79181 q - 104 q^{2} - 78 q^{3} - 104 q^{4} - 128 q^{5} - 168 q^{6} - 76 q^{7} - 104 q^{8} - 121 q^{9} - 128 q^{10} - 110 q^{11} - 104 q^{12} - 88 q^{13} - 104 q^{14} - 96 q^{15} - 168 q^{16} - 198 q^{17} - 104 q^{18} - 110 q^{19} - 128 q^{20} - 252 q^{21} - 176 q^{22} - 140 q^{23} - 384 q^{24} - 160 q^{25} - 528 q^{26} - 144 q^{27} - 224 q^{28} - 136 q^{29} - 128 q^{30} - 136 q^{31} - 64 q^{32} + 4 q^{33} + 16 q^{34} - 96 q^{35} + 232 q^{36} + 72 q^{37} + 176 q^{38} + 100 q^{39} - 128 q^{40} + 46 q^{41} + 336 q^{42} + 34 q^{43} - 128 q^{45} - 168 q^{46} - 80 q^{47} - 104 q^{48} - 263 q^{49} - 128 q^{50} - 788 q^{51} + 424 q^{52} - 248 q^{53} + 472 q^{54} - 96 q^{55} + 224 q^{56} - 512 q^{57} + 256 q^{58} - 542 q^{59} - 128 q^{60} - 280 q^{61} - 88 q^{62} - 856 q^{63} - 200 q^{64} - 800 q^{65} - 424 q^{66} - 686 q^{67} - 344 q^{68} - 1820 q^{69} - 128 q^{70} - 380 q^{71} - 752 q^{72} - 642 q^{73} - 720 q^{74} - 544 q^{75} - 1160 q^{76} - 636 q^{77} - 1232 q^{78} + 448 q^{79} - 128 q^{80} - 195 q^{81} - 1144 q^{82} + 242 q^{83} - 1336 q^{84} + 448 q^{85} - 1104 q^{86} + 1268 q^{87} - 664 q^{88} + 606 q^{89} - 128 q^{90} + 1220 q^{91} - 560 q^{92} + 2224 q^{93} - 200 q^{94} + 672 q^{95} - 32 q^{96} + 1282 q^{97} + 304 q^{98} + 1514 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1600))\)

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
1600.3.b \(\chi_{1600}(1151, \cdot)\) 1600.3.b.a 1 1
1600.3.b.b 1
1600.3.b.c 1
1600.3.b.d 2
1600.3.b.e 2
1600.3.b.f 2
1600.3.b.g 2
1600.3.b.h 2
1600.3.b.i 2
1600.3.b.j 2
1600.3.b.k 4
1600.3.b.l 4
1600.3.b.m 4
1600.3.b.n 4
1600.3.b.o 4
1600.3.b.p 4
1600.3.b.q 4
1600.3.b.r 4
1600.3.b.s 4
1600.3.b.t 4
1600.3.b.u 4
1600.3.b.v 6
1600.3.b.w 6
1600.3.e \(\chi_{1600}(799, \cdot)\) 1600.3.e.a 4 1
1600.3.e.b 4
1600.3.e.c 4
1600.3.e.d 4
1600.3.e.e 4
1600.3.e.f 4
1600.3.e.g 8
1600.3.e.h 8
1600.3.e.i 8
1600.3.e.j 8
1600.3.e.k 8
1600.3.e.l 8
1600.3.g \(\chi_{1600}(351, \cdot)\) 1600.3.g.a 4 1
1600.3.g.b 4
1600.3.g.c 4
1600.3.g.d 4
1600.3.g.e 4
1600.3.g.f 8
1600.3.g.g 8
1600.3.g.h 8
1600.3.g.i 8
1600.3.g.j 8
1600.3.g.k 16
1600.3.h \(\chi_{1600}(1599, \cdot)\) 1600.3.h.a 2 1
1600.3.h.b 2
1600.3.h.c 2
1600.3.h.d 4
1600.3.h.e 4
1600.3.h.f 4
1600.3.h.g 4
1600.3.h.h 4
1600.3.h.i 4
1600.3.h.j 4
1600.3.h.k 4
1600.3.h.l 4
1600.3.h.m 4
1600.3.h.n 8
1600.3.h.o 8
1600.3.h.p 8
1600.3.i \(\chi_{1600}(593, \cdot)\) n/a 140 2
1600.3.k \(\chi_{1600}(399, \cdot)\) n/a 140 2
1600.3.m \(\chi_{1600}(993, \cdot)\) n/a 144 2
1600.3.p \(\chi_{1600}(193, \cdot)\) n/a 140 2
1600.3.r \(\chi_{1600}(751, \cdot)\) n/a 146 2
1600.3.t \(\chi_{1600}(657, \cdot)\) n/a 140 2
1600.3.w \(\chi_{1600}(57, \cdot)\) None 0 4
1600.3.x \(\chi_{1600}(151, \cdot)\) None 0 4
1600.3.z \(\chi_{1600}(199, \cdot)\) None 0 4
1600.3.bc \(\chi_{1600}(457, \cdot)\) None 0 4
1600.3.bd \(\chi_{1600}(31, \cdot)\) n/a 480 4
1600.3.bf \(\chi_{1600}(319, \cdot)\) n/a 472 4
1600.3.bh \(\chi_{1600}(191, \cdot)\) n/a 472 4
1600.3.bi \(\chi_{1600}(159, \cdot)\) n/a 480 4
1600.3.bk \(\chi_{1600}(157, \cdot)\) n/a 2288 8
1600.3.bo \(\chi_{1600}(51, \cdot)\) n/a 2408 8
1600.3.bp \(\chi_{1600}(99, \cdot)\) n/a 2288 8
1600.3.bq \(\chi_{1600}(93, \cdot)\) n/a 2288 8
1600.3.bs \(\chi_{1600}(17, \cdot)\) n/a 944 8
1600.3.bv \(\chi_{1600}(79, \cdot)\) n/a 944 8
1600.3.bw \(\chi_{1600}(513, \cdot)\) n/a 944 8
1600.3.bz \(\chi_{1600}(33, \cdot)\) n/a 960 8
1600.3.ca \(\chi_{1600}(111, \cdot)\) n/a 944 8
1600.3.cd \(\chi_{1600}(177, \cdot)\) n/a 944 8
1600.3.ce \(\chi_{1600}(73, \cdot)\) None 0 16
1600.3.ch \(\chi_{1600}(39, \cdot)\) None 0 16
1600.3.cj \(\chi_{1600}(71, \cdot)\) None 0 16
1600.3.ck \(\chi_{1600}(137, \cdot)\) None 0 16
1600.3.cn \(\chi_{1600}(13, \cdot)\) n/a 15296 32
1600.3.co \(\chi_{1600}(19, \cdot)\) n/a 15296 32
1600.3.cp \(\chi_{1600}(11, \cdot)\) n/a 15296 32
1600.3.ct \(\chi_{1600}(53, \cdot)\) n/a 15296 32

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1600))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1600)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)