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Properties

Label 147.6
Level 147
Weight 6
Dimension 2773
Nonzero newspaces 8
Sturm bound 9408
Trace bound 1

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Defining parameters

Level: \( N \) = \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(9408\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(147))\).

Total New Old
Modular forms 4040 2869 1171
Cusp forms 3800 2773 1027
Eisenstein series 240 96 144

Trace form

\( 2773 q - 6 q^{2} - 24 q^{3} + 230 q^{4} - 126 q^{5} - 507 q^{6} - 268 q^{7} - 516 q^{8} + 1368 q^{9} + O(q^{10}) \) \( 2773 q - 6 q^{2} - 24 q^{3} + 230 q^{4} - 126 q^{5} - 507 q^{6} - 268 q^{7} - 516 q^{8} + 1368 q^{9} + 6114 q^{10} + 264 q^{11} - 4209 q^{12} - 6096 q^{13} - 3720 q^{14} - 4737 q^{15} + 3010 q^{16} + 7386 q^{17} + 14505 q^{18} - 4050 q^{19} + 10032 q^{20} + 5673 q^{21} + 15402 q^{22} + 14472 q^{23} - 17949 q^{24} - 41003 q^{25} - 34488 q^{26} - 5124 q^{27} - 11028 q^{28} - 2778 q^{29} + 43035 q^{30} + 16794 q^{31} - 732 q^{32} - 20001 q^{33} + 42930 q^{34} + 13398 q^{35} - 129831 q^{36} + 73724 q^{37} - 70548 q^{38} - 25974 q^{39} - 290730 q^{40} - 76890 q^{41} - 35859 q^{42} - 58718 q^{43} + 43776 q^{44} + 80151 q^{45} + 367950 q^{46} + 217944 q^{47} + 243216 q^{48} + 418818 q^{49} + 208986 q^{50} - 58359 q^{51} - 195842 q^{52} - 156318 q^{53} - 233463 q^{54} - 1006824 q^{55} - 964338 q^{56} - 241725 q^{57} - 317502 q^{58} - 100152 q^{59} + 315339 q^{60} + 539950 q^{61} + 802248 q^{62} + 276660 q^{63} + 1186598 q^{64} + 455880 q^{65} + 515679 q^{66} + 19190 q^{67} - 190392 q^{68} - 236109 q^{69} - 731706 q^{70} - 607632 q^{71} - 1247097 q^{72} - 702000 q^{73} - 619584 q^{74} - 780030 q^{75} - 256170 q^{76} + 150624 q^{77} + 736917 q^{78} + 1216538 q^{79} + 3099246 q^{80} + 1030500 q^{81} + 1608936 q^{82} + 40116 q^{83} - 813726 q^{84} - 760986 q^{85} - 2334978 q^{86} - 684303 q^{87} - 3090564 q^{88} - 862662 q^{89} - 1286208 q^{90} - 299914 q^{91} - 1092210 q^{92} - 1100781 q^{93} - 35772 q^{94} + 1218900 q^{95} + 988008 q^{96} + 2165418 q^{97} + 5299410 q^{98} + 584928 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.6.a \(\chi_{147}(1, \cdot)\) 147.6.a.a 1 1
147.6.a.b 1
147.6.a.c 1
147.6.a.d 1
147.6.a.e 1
147.6.a.f 1
147.6.a.g 1
147.6.a.h 2
147.6.a.i 2
147.6.a.j 2
147.6.a.k 2
147.6.a.l 4
147.6.a.m 4
147.6.a.n 6
147.6.a.o 6
147.6.c \(\chi_{147}(146, \cdot)\) 147.6.c.a 2 1
147.6.c.b 4
147.6.c.c 16
147.6.c.d 40
147.6.e \(\chi_{147}(67, \cdot)\) 147.6.e.a 2 2
147.6.e.b 2
147.6.e.c 2
147.6.e.d 2
147.6.e.e 2
147.6.e.f 2
147.6.e.g 2
147.6.e.h 2
147.6.e.i 2
147.6.e.j 2
147.6.e.k 2
147.6.e.l 4
147.6.e.m 4
147.6.e.n 4
147.6.e.o 8
147.6.e.p 12
147.6.e.q 12
147.6.g \(\chi_{147}(68, \cdot)\) n/a 126 2
147.6.i \(\chi_{147}(22, \cdot)\) n/a 276 6
147.6.k \(\chi_{147}(20, \cdot)\) n/a 552 6
147.6.m \(\chi_{147}(4, \cdot)\) n/a 564 12
147.6.o \(\chi_{147}(5, \cdot)\) n/a 1092 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(147)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)