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Properties

Label 147.10
Level 147
Weight 10
Dimension 5030
Nonzero newspaces 8
Sturm bound 15680
Trace bound 1

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Defining parameters

Level: \( N \) = \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(15680\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(147))\).

Total New Old
Modular forms 7176 5126 2050
Cusp forms 6936 5030 1906
Eisenstein series 240 96 144

Trace form

\( 5030 q - 18 q^{2} + 309 q^{3} + 566 q^{4} + 564 q^{5} - 11199 q^{6} + 2700 q^{7} + 181404 q^{8} - 88281 q^{9} + O(q^{10}) \) \( 5030 q - 18 q^{2} + 309 q^{3} + 566 q^{4} + 564 q^{5} - 11199 q^{6} + 2700 q^{7} + 181404 q^{8} - 88281 q^{9} - 180966 q^{10} + 318960 q^{11} + 90111 q^{12} - 1195046 q^{13} - 331656 q^{14} + 1661613 q^{15} + 3037634 q^{16} + 181308 q^{17} - 4709091 q^{18} - 261302 q^{19} + 3581712 q^{20} + 800418 q^{21} - 10685190 q^{22} + 8280096 q^{23} - 563421 q^{24} + 15564632 q^{25} - 6864672 q^{26} - 4251549 q^{27} - 31232148 q^{28} + 8734644 q^{29} + 54229155 q^{30} + 86972026 q^{31} + 52236516 q^{32} - 3645363 q^{33} - 179270118 q^{34} - 64657572 q^{35} - 211799895 q^{36} + 12816982 q^{37} + 100595532 q^{38} + 117791613 q^{39} + 653999190 q^{40} + 45851076 q^{41} - 113181339 q^{42} - 107219654 q^{43} - 444129792 q^{44} - 233013999 q^{45} + 64521246 q^{46} - 95615448 q^{47} + 577312272 q^{48} + 792563976 q^{49} + 704553126 q^{50} + 435161517 q^{51} - 849144098 q^{52} - 595647012 q^{53} - 907020795 q^{54} - 1537268574 q^{55} + 1027261518 q^{56} - 258694131 q^{57} + 812120442 q^{58} + 642764184 q^{59} + 599883819 q^{60} - 543813770 q^{61} + 596910168 q^{62} + 567502326 q^{63} + 3582051110 q^{64} - 1373278680 q^{65} - 2863657425 q^{66} - 2678157302 q^{67} - 1357471704 q^{68} - 1152337125 q^{69} - 77470746 q^{70} - 21443736 q^{71} + 4109504199 q^{72} + 1675201654 q^{73} + 3846220536 q^{74} + 546370875 q^{75} + 1289379478 q^{76} - 250274628 q^{77} - 6919773411 q^{78} - 4624830278 q^{79} - 2181537234 q^{80} - 1315139805 q^{81} - 9378061680 q^{82} + 2204987112 q^{83} + 16136693730 q^{84} + 13665125994 q^{85} + 14385021774 q^{86} - 2955391845 q^{87} - 17165496708 q^{88} - 10148028468 q^{89} - 28669763448 q^{90} - 11311745766 q^{91} - 11171252274 q^{92} + 2119646169 q^{93} + 18776975076 q^{94} + 17148960720 q^{95} + 27341274696 q^{96} + 10266801604 q^{97} + 38742936306 q^{98} - 6947009928 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(147))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
147.10.a \(\chi_{147}(1, \cdot)\) 147.10.a.a 1 1
147.10.a.b 1
147.10.a.c 1
147.10.a.d 2
147.10.a.e 2
147.10.a.f 3
147.10.a.g 4
147.10.a.h 4
147.10.a.i 5
147.10.a.j 5
147.10.a.k 7
147.10.a.l 7
147.10.a.m 10
147.10.a.n 10
147.10.c \(\chi_{147}(146, \cdot)\) n/a 116 1
147.10.e \(\chi_{147}(67, \cdot)\) n/a 120 2
147.10.g \(\chi_{147}(68, \cdot)\) n/a 232 2
147.10.i \(\chi_{147}(22, \cdot)\) n/a 504 6
147.10.k \(\chi_{147}(20, \cdot)\) n/a 996 6
147.10.m \(\chi_{147}(4, \cdot)\) n/a 1008 12
147.10.o \(\chi_{147}(5, \cdot)\) n/a 1992 12

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(147)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)