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Properties

Label 147.3
Level 147
Weight 3
Dimension 1080
Nonzero newspaces 8
Newform subspaces 30
Sturm bound 4704
Trace bound 1

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Defining parameters

Level: \( N \) = \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 30 \)
Sturm bound: \(4704\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(147))\).

Total New Old
Modular forms 1688 1178 510
Cusp forms 1448 1080 368
Eisenstein series 240 98 142

Trace form

\( 1080 q - 9 q^{3} + 2 q^{4} + 12 q^{5} - 9 q^{6} - 44 q^{7} + 12 q^{8} + 27 q^{9} + O(q^{10}) \) \( 1080 q - 9 q^{3} + 2 q^{4} + 12 q^{5} - 9 q^{6} - 44 q^{7} + 12 q^{8} + 27 q^{9} - 18 q^{10} - 12 q^{11} - 57 q^{12} - 46 q^{13} - 24 q^{14} - 135 q^{15} - 222 q^{16} - 96 q^{17} - 213 q^{18} - 46 q^{19} + 3 q^{21} + 138 q^{22} + 192 q^{23} + 279 q^{24} + 222 q^{25} + 252 q^{26} + 243 q^{27} + 60 q^{28} + 24 q^{29} - 69 q^{30} - 214 q^{31} - 156 q^{32} - 393 q^{33} - 522 q^{34} - 210 q^{35} - 435 q^{36} - 978 q^{37} - 1188 q^{38} - 594 q^{39} - 2250 q^{40} - 588 q^{41} - 453 q^{42} - 122 q^{43} - 672 q^{44} + 249 q^{45} - 138 q^{46} + 360 q^{47} + 378 q^{48} + 246 q^{49} + 564 q^{50} + 567 q^{51} + 886 q^{52} + 444 q^{53} + 147 q^{54} + 1116 q^{55} + 1998 q^{56} + 123 q^{57} + 1638 q^{58} + 756 q^{59} + 1299 q^{60} + 1156 q^{61} + 1176 q^{62} + 6 q^{63} + 1142 q^{64} - 36 q^{65} + 51 q^{66} - 246 q^{67} - 72 q^{68} - 597 q^{69} + 18 q^{70} - 240 q^{71} - 369 q^{72} + 158 q^{73} - 180 q^{74} - 381 q^{75} + 542 q^{76} - 72 q^{77} - 735 q^{78} - 366 q^{79} - 2238 q^{80} - 1365 q^{81} - 3408 q^{82} - 2352 q^{83} - 3126 q^{84} - 1758 q^{85} - 3654 q^{86} - 1725 q^{87} - 4152 q^{88} - 1224 q^{89} - 2550 q^{90} - 902 q^{91} - 1302 q^{92} - 501 q^{93} - 528 q^{94} + 204 q^{95} + 510 q^{96} + 668 q^{97} + 858 q^{98} + 1140 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.3.b \(\chi_{147}(50, \cdot)\) 147.3.b.a 1 1
147.3.b.b 1
147.3.b.c 2
147.3.b.d 2
147.3.b.e 4
147.3.b.f 4
147.3.b.g 8
147.3.d \(\chi_{147}(97, \cdot)\) 147.3.d.a 2 1
147.3.d.b 2
147.3.d.c 2
147.3.d.d 8
147.3.f \(\chi_{147}(19, \cdot)\) 147.3.f.a 2 2
147.3.f.b 2
147.3.f.c 2
147.3.f.d 2
147.3.f.e 2
147.3.f.f 8
147.3.f.g 8
147.3.h \(\chi_{147}(116, \cdot)\) 147.3.h.a 2 2
147.3.h.b 4
147.3.h.c 8
147.3.h.d 8
147.3.h.e 8
147.3.h.f 16
147.3.j \(\chi_{147}(13, \cdot)\) 147.3.j.a 108 6
147.3.l \(\chi_{147}(8, \cdot)\) 147.3.l.a 216 6
147.3.n \(\chi_{147}(2, \cdot)\) 147.3.n.a 12 12
147.3.n.b 408
147.3.p \(\chi_{147}(10, \cdot)\) 147.3.p.a 108 12
147.3.p.b 120

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(147)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 1}\)