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Properties

Label 147.5
Level 147
Weight 5
Dimension 2208
Nonzero newspaces 8
Newform subspaces 30
Sturm bound 7840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 30 \)
Sturm bound: \(7840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(147))\).

Total New Old
Modular forms 3256 2306 950
Cusp forms 3016 2208 808
Eisenstein series 240 98 142

Trace form

\( 2208 q + 3 q^{3} - 158 q^{4} - 108 q^{5} - 9 q^{6} + 68 q^{7} + 1116 q^{8} - 57 q^{9} + O(q^{10}) \) \( 2208 q + 3 q^{3} - 158 q^{4} - 108 q^{5} - 9 q^{6} + 68 q^{7} + 1116 q^{8} - 57 q^{9} - 834 q^{10} - 1044 q^{11} - 1377 q^{12} - 662 q^{13} + 648 q^{14} + 1521 q^{15} + 3090 q^{16} + 1728 q^{17} + 3171 q^{18} + 3586 q^{19} - 1803 q^{21} - 9750 q^{22} - 5760 q^{23} - 7785 q^{24} - 3306 q^{25} - 756 q^{26} - 1269 q^{27} - 276 q^{28} + 1224 q^{29} + 1947 q^{30} + 7930 q^{31} + 3060 q^{32} + 4899 q^{33} + 9558 q^{34} + 2394 q^{35} + 26541 q^{36} - 24090 q^{37} - 20700 q^{38} + 6468 q^{39} + 34326 q^{40} + 19404 q^{41} + 24747 q^{42} + 26270 q^{43} + 63504 q^{44} - 9471 q^{45} + 10734 q^{46} - 23400 q^{47} - 55062 q^{48} - 32934 q^{49} - 45324 q^{50} - 41877 q^{51} - 103258 q^{52} - 38988 q^{53} + 27363 q^{54} - 19800 q^{55} - 60498 q^{56} + 30975 q^{57} + 41622 q^{58} + 32508 q^{59} + 70275 q^{60} + 70832 q^{61} + 84672 q^{62} + 22938 q^{63} - 6362 q^{64} - 14796 q^{65} - 64245 q^{66} - 71238 q^{67} - 85032 q^{68} - 95853 q^{69} - 62478 q^{70} - 58608 q^{71} - 56673 q^{72} + 34918 q^{73} + 108828 q^{74} + 94611 q^{75} + 172798 q^{76} + 32184 q^{77} + 145353 q^{78} + 78930 q^{79} - 139518 q^{80} - 32289 q^{81} - 185208 q^{82} - 70560 q^{83} - 28242 q^{84} - 57390 q^{85} + 44226 q^{86} - 25125 q^{87} + 214152 q^{88} + 103752 q^{89} + 135294 q^{90} + 133610 q^{91} + 110250 q^{92} + 122463 q^{93} + 292392 q^{94} + 165924 q^{95} + 190122 q^{96} + 75484 q^{97} - 87678 q^{98} + 79692 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.5.b \(\chi_{147}(50, \cdot)\) 147.5.b.a 1 1
147.5.b.b 1
147.5.b.c 8
147.5.b.d 8
147.5.b.e 8
147.5.b.f 8
147.5.b.g 16
147.5.d \(\chi_{147}(97, \cdot)\) 147.5.d.a 2 1
147.5.d.b 2
147.5.d.c 6
147.5.d.d 16
147.5.f \(\chi_{147}(19, \cdot)\) 147.5.f.a 2 2
147.5.f.b 2
147.5.f.c 6
147.5.f.d 6
147.5.f.e 6
147.5.f.f 16
147.5.f.g 16
147.5.h \(\chi_{147}(116, \cdot)\) 147.5.h.a 2 2
147.5.h.b 16
147.5.h.c 16
147.5.h.d 16
147.5.h.e 16
147.5.h.f 32
147.5.j \(\chi_{147}(13, \cdot)\) 147.5.j.a 228 6
147.5.l \(\chi_{147}(8, \cdot)\) 147.5.l.a 432 6
147.5.n \(\chi_{147}(2, \cdot)\) 147.5.n.a 12 12
147.5.n.b 864
147.5.p \(\chi_{147}(10, \cdot)\) 147.5.p.a 216 12
147.5.p.b 228

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(147)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)