Properties

Label 147.4
Level 147
Weight 4
Dimension 1644
Nonzero newspaces 8
Newform subspaces 41
Sturm bound 6272
Trace bound 1

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Defining parameters

Level: \( N \) = \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 41 \)
Sturm bound: \(6272\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(147))\).

Total New Old
Modular forms 2472 1740 732
Cusp forms 2232 1644 588
Eisenstein series 240 96 144

Trace form

\( 1644q - 27q^{3} - 30q^{4} + 48q^{5} + 51q^{6} + 12q^{7} - 108q^{8} - 99q^{9} + O(q^{10}) \) \( 1644q - 27q^{3} - 30q^{4} + 48q^{5} + 51q^{6} + 12q^{7} - 108q^{8} - 99q^{9} - 138q^{10} + 171q^{12} + 126q^{13} + 312q^{14} + 357q^{15} + 210q^{16} + 24q^{17} - 561q^{18} - 1158q^{19} - 2088q^{20} - 606q^{21} - 942q^{22} + 336q^{23} - 309q^{24} + 810q^{25} + 588q^{26} + 195q^{27} + 1068q^{28} + 1296q^{29} + 3039q^{30} + 1458q^{31} + 2436q^{32} + 1581q^{33} + 510q^{34} - 84q^{35} - 555q^{36} + 1818q^{37} + 1788q^{38} - 387q^{39} + 3174q^{40} + 288q^{41} - 2847q^{42} - 3894q^{43} - 11424q^{44} - 5835q^{45} - 12042q^{46} - 5448q^{47} - 5280q^{48} - 5760q^{49} - 1212q^{50} + 2589q^{51} - 1770q^{52} + 1848q^{53} + 8295q^{54} + 738q^{55} + 1326q^{56} + 1269q^{57} - 42q^{58} + 5880q^{59} + 4443q^{60} + 4266q^{61} + 7632q^{62} - 1170q^{63} + 582q^{64} - 1008q^{65} - 1785q^{66} - 1878q^{67} + 3072q^{68} + 3291q^{69} + 3462q^{70} + 984q^{71} + 8079q^{72} + 8610q^{73} + 5460q^{74} + 4587q^{75} + 11046q^{76} + 180q^{77} + 2841q^{78} + 978q^{79} + 20142q^{80} + 6705q^{81} + 15012q^{82} + 10584q^{83} + 11658q^{84} + 498q^{85} - 42q^{86} - 1149q^{87} + 348q^{88} - 696q^{89} - 14220q^{90} - 10086q^{91} - 10290q^{92} - 18159q^{93} - 33180q^{94} - 33264q^{95} - 28704q^{96} - 16896q^{97} - 51054q^{98} - 7128q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.4.a \(\chi_{147}(1, \cdot)\) 147.4.a.a 1 1
147.4.a.b 1
147.4.a.c 1
147.4.a.d 1
147.4.a.e 1
147.4.a.f 1
147.4.a.g 1
147.4.a.h 1
147.4.a.i 2
147.4.a.j 2
147.4.a.k 2
147.4.a.l 3
147.4.a.m 3
147.4.c \(\chi_{147}(146, \cdot)\) 147.4.c.a 12 1
147.4.c.b 24
147.4.e \(\chi_{147}(67, \cdot)\) 147.4.e.a 2 2
147.4.e.b 2
147.4.e.c 2
147.4.e.d 2
147.4.e.e 2
147.4.e.f 2
147.4.e.g 2
147.4.e.h 2
147.4.e.i 2
147.4.e.j 4
147.4.e.k 4
147.4.e.l 4
147.4.e.m 4
147.4.e.n 6
147.4.g \(\chi_{147}(68, \cdot)\) 147.4.g.a 2 2
147.4.g.b 2
147.4.g.c 8
147.4.g.d 12
147.4.g.e 48
147.4.i \(\chi_{147}(22, \cdot)\) 147.4.i.a 84 6
147.4.i.b 84
147.4.k \(\chi_{147}(20, \cdot)\) 147.4.k.a 12 6
147.4.k.b 312
147.4.m \(\chi_{147}(4, \cdot)\) 147.4.m.a 156 12
147.4.m.b 180
147.4.o \(\chi_{147}(5, \cdot)\) 147.4.o.a 648 12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

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