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Properties

Label 1550.3
Level 1550
Weight 3
Dimension 44148
Nonzero newspaces 42
Sturm bound 432000
Trace bound 12

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Defining parameters

Level: \( N \) = \( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 42 \)
Sturm bound: \(432000\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1550))\).

Total New Old
Modular forms 145680 44148 101532
Cusp forms 142320 44148 98172
Eisenstein series 3360 0 3360

Trace form

\( 44148 q - 8 q^{2} - 16 q^{3} + 32 q^{6} + 16 q^{7} + 16 q^{8} + O(q^{10}) \) \( 44148 q - 8 q^{2} - 16 q^{3} + 32 q^{6} + 16 q^{7} + 16 q^{8} - 20 q^{10} - 64 q^{11} - 32 q^{12} + 24 q^{13} + 40 q^{15} - 32 q^{16} + 336 q^{17} + 308 q^{18} + 400 q^{19} + 80 q^{20} + 86 q^{21} - 16 q^{22} - 146 q^{23} - 220 q^{25} - 248 q^{26} - 790 q^{27} - 272 q^{28} - 460 q^{29} - 480 q^{30} - 12 q^{31} - 48 q^{32} - 412 q^{33} - 260 q^{34} - 400 q^{35} + 224 q^{36} + 726 q^{37} + 80 q^{38} + 1430 q^{39} - 40 q^{40} + 586 q^{41} + 424 q^{42} + 274 q^{43} + 660 q^{45} + 32 q^{46} + 16 q^{47} + 64 q^{48} - 360 q^{49} + 100 q^{50} - 1364 q^{51} + 48 q^{52} - 176 q^{53} - 480 q^{55} + 64 q^{56} - 1320 q^{57} + 320 q^{58} - 260 q^{59} + 480 q^{60} + 176 q^{61} + 512 q^{62} + 1304 q^{63} + 1580 q^{65} + 704 q^{66} + 1796 q^{67} + 608 q^{68} + 2120 q^{69} + 560 q^{70} + 856 q^{71} + 16 q^{72} + 144 q^{73} - 120 q^{75} - 1958 q^{77} - 1964 q^{78} - 1710 q^{79} - 1872 q^{81} - 1816 q^{82} - 3626 q^{83} - 1680 q^{84} - 920 q^{85} - 1488 q^{86} - 2880 q^{87} - 368 q^{88} - 3350 q^{89} - 1940 q^{90} - 754 q^{91} - 752 q^{92} - 316 q^{93} + 120 q^{94} - 80 q^{95} - 128 q^{96} + 226 q^{97} + 752 q^{98} + 1050 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1550))\)

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
1550.3.c \(\chi_{1550}(1301, \cdot)\) 1550.3.c.a 4 1
1550.3.c.b 20
1550.3.c.c 20
1550.3.c.d 24
1550.3.c.e 32
1550.3.d \(\chi_{1550}(1549, \cdot)\) 1550.3.d.a 8 1
1550.3.d.b 40
1550.3.d.c 48
1550.3.g \(\chi_{1550}(807, \cdot)\) n/a 180 2
1550.3.n \(\chi_{1550}(99, \cdot)\) n/a 192 2
1550.3.o \(\chi_{1550}(801, \cdot)\) n/a 204 2
1550.3.q \(\chi_{1550}(1021, \cdot)\) n/a 640 4
1550.3.s \(\chi_{1550}(309, \cdot)\) n/a 640 4
1550.3.t \(\chi_{1550}(89, \cdot)\) n/a 640 4
1550.3.u \(\chi_{1550}(139, \cdot)\) n/a 640 4
1550.3.v \(\chi_{1550}(399, \cdot)\) n/a 384 4
1550.3.w \(\chi_{1550}(339, \cdot)\) n/a 640 4
1550.3.y \(\chi_{1550}(581, \cdot)\) n/a 640 4
1550.3.z \(\chi_{1550}(461, \cdot)\) n/a 640 4
1550.3.ba \(\chi_{1550}(151, \cdot)\) n/a 400 4
1550.3.bb \(\chi_{1550}(91, \cdot)\) n/a 640 4
1550.3.bg \(\chi_{1550}(61, \cdot)\) n/a 640 4
1550.3.bh \(\chi_{1550}(29, \cdot)\) n/a 640 4
1550.3.bi \(\chi_{1550}(707, \cdot)\) n/a 384 4
1550.3.br \(\chi_{1550}(233, \cdot)\) n/a 1280 8
1550.3.bs \(\chi_{1550}(63, \cdot)\) n/a 1200 8
1550.3.bt \(\chi_{1550}(97, \cdot)\) n/a 1280 8
1550.3.bu \(\chi_{1550}(157, \cdot)\) n/a 768 8
1550.3.bv \(\chi_{1550}(283, \cdot)\) n/a 1280 8
1550.3.bw \(\chi_{1550}(33, \cdot)\) n/a 1280 8
1550.3.cc \(\chi_{1550}(229, \cdot)\) n/a 1280 8
1550.3.cd \(\chi_{1550}(161, \cdot)\) n/a 1280 8
1550.3.ci \(\chi_{1550}(261, \cdot)\) n/a 1280 8
1550.3.cj \(\chi_{1550}(251, \cdot)\) n/a 816 8
1550.3.ck \(\chi_{1550}(11, \cdot)\) n/a 1280 8
1550.3.cl \(\chi_{1550}(321, \cdot)\) n/a 1280 8
1550.3.cn \(\chi_{1550}(179, \cdot)\) n/a 1280 8
1550.3.co \(\chi_{1550}(199, \cdot)\) n/a 768 8
1550.3.cp \(\chi_{1550}(79, \cdot)\) n/a 1280 8
1550.3.cq \(\chi_{1550}(269, \cdot)\) n/a 1280 8
1550.3.cr \(\chi_{1550}(119, \cdot)\) n/a 1280 8
1550.3.ct \(\chi_{1550}(21, \cdot)\) n/a 1280 8
1550.3.cz \(\chi_{1550}(267, \cdot)\) n/a 2560 16
1550.3.da \(\chi_{1550}(173, \cdot)\) n/a 2560 16
1550.3.db \(\chi_{1550}(7, \cdot)\) n/a 1536 16
1550.3.dc \(\chi_{1550}(133, \cdot)\) n/a 2560 16
1550.3.dd \(\chi_{1550}(67, \cdot)\) n/a 2560 16
1550.3.de \(\chi_{1550}(103, \cdot)\) n/a 2560 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1550))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1550)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(775))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1550))\)\(^{\oplus 1}\)