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Properties

Label 620.3
Level 620
Weight 3
Dimension 12120
Nonzero newspaces 24
Sturm bound 69120
Trace bound 4

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Defining parameters

Level: \( N \) = \( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(69120\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(620))\).

Total New Old
Modular forms 23640 12472 11168
Cusp forms 22440 12120 10320
Eisenstein series 1200 352 848

Trace form

\( 12120 q - 26 q^{2} - 4 q^{3} - 22 q^{4} - 70 q^{5} - 58 q^{6} + 28 q^{7} - 14 q^{8} - 44 q^{9} + O(q^{10}) \) \( 12120 q - 26 q^{2} - 4 q^{3} - 22 q^{4} - 70 q^{5} - 58 q^{6} + 28 q^{7} - 14 q^{8} - 44 q^{9} - 57 q^{10} - 40 q^{11} - 110 q^{12} - 64 q^{13} - 142 q^{14} - 4 q^{15} - 186 q^{16} - 16 q^{17} - 74 q^{18} + 43 q^{20} - 230 q^{21} + 130 q^{22} - 118 q^{23} + 258 q^{24} - 224 q^{25} + 126 q^{26} - 334 q^{27} + 50 q^{28} - 184 q^{29} - 110 q^{30} + 88 q^{31} - 316 q^{32} - 80 q^{33} - 342 q^{34} - 46 q^{35} - 274 q^{36} + 406 q^{37} - 190 q^{38} + 630 q^{39} + 3 q^{40} + 254 q^{41} + 210 q^{42} + 190 q^{43} + 130 q^{44} + 350 q^{45} + 182 q^{46} + 156 q^{47} + 1140 q^{48} + 996 q^{49} + 608 q^{50} + 1792 q^{51} + 1208 q^{52} + 800 q^{53} + 2056 q^{54} + 480 q^{55} + 972 q^{56} + 692 q^{57} + 672 q^{58} + 120 q^{59} + 100 q^{60} - 400 q^{61} - 130 q^{62} - 676 q^{63} - 442 q^{64} - 950 q^{65} - 2500 q^{66} - 332 q^{67} - 1228 q^{68} - 2444 q^{69} - 1100 q^{70} - 1592 q^{71} - 3516 q^{72} - 1504 q^{73} - 1572 q^{74} - 1391 q^{75} - 2340 q^{76} - 2570 q^{77} - 1400 q^{78} - 910 q^{79} + 243 q^{80} - 768 q^{81} - 262 q^{82} - 1638 q^{83} - 94 q^{84} + 94 q^{85} - 538 q^{86} - 568 q^{87} - 350 q^{88} + 546 q^{89} + 48 q^{90} + 374 q^{91} + 240 q^{92} + 608 q^{93} + 148 q^{94} + 232 q^{95} + 152 q^{96} + 986 q^{97} - 234 q^{98} + 1050 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(620))\)

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
620.3.b \(\chi_{620}(311, \cdot)\) n/a 120 1
620.3.d \(\chi_{620}(61, \cdot)\) 620.3.d.a 20 1
620.3.f \(\chi_{620}(309, \cdot)\) 620.3.f.a 4 1
620.3.f.b 4
620.3.f.c 24
620.3.h \(\chi_{620}(559, \cdot)\) n/a 180 1
620.3.l \(\chi_{620}(373, \cdot)\) 620.3.l.a 60 2
620.3.m \(\chi_{620}(123, \cdot)\) n/a 376 2
620.3.o \(\chi_{620}(439, \cdot)\) n/a 376 2
620.3.q \(\chi_{620}(409, \cdot)\) 620.3.q.a 64 2
620.3.s \(\chi_{620}(161, \cdot)\) 620.3.s.a 44 2
620.3.u \(\chi_{620}(191, \cdot)\) n/a 256 2
620.3.v \(\chi_{620}(39, \cdot)\) n/a 752 4
620.3.x \(\chi_{620}(29, \cdot)\) n/a 128 4
620.3.z \(\chi_{620}(201, \cdot)\) 620.3.z.a 40 4
620.3.z.b 40
620.3.bb \(\chi_{620}(171, \cdot)\) n/a 512 4
620.3.bc \(\chi_{620}(223, \cdot)\) n/a 752 4
620.3.bd \(\chi_{620}(253, \cdot)\) n/a 128 4
620.3.bh \(\chi_{620}(23, \cdot)\) n/a 1504 8
620.3.bi \(\chi_{620}(33, \cdot)\) n/a 256 8
620.3.bl \(\chi_{620}(51, \cdot)\) n/a 1024 8
620.3.bn \(\chi_{620}(21, \cdot)\) n/a 176 8
620.3.bp \(\chi_{620}(189, \cdot)\) n/a 256 8
620.3.br \(\chi_{620}(19, \cdot)\) n/a 1504 8
620.3.bu \(\chi_{620}(113, \cdot)\) n/a 512 16
620.3.bv \(\chi_{620}(3, \cdot)\) n/a 3008 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(620))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(620)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 1}\)