Properties

Label 153.4
Level 153
Weight 4
Dimension 1970
Nonzero newspaces 10
Newform subspaces 27
Sturm bound 6912
Trace bound 1

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Defining parameters

Level: \( N \) = \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 27 \)
Sturm bound: \(6912\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(153))\).

Total New Old
Modular forms 2720 2104 616
Cusp forms 2464 1970 494
Eisenstein series 256 134 122

Trace form

\( 1970 q - 18 q^{2} - 26 q^{3} + 2 q^{4} + 6 q^{5} - 50 q^{6} - 50 q^{7} - 156 q^{8} - 122 q^{9} + O(q^{10}) \) \( 1970 q - 18 q^{2} - 26 q^{3} + 2 q^{4} + 6 q^{5} - 50 q^{6} - 50 q^{7} - 156 q^{8} - 122 q^{9} - 200 q^{10} - 4 q^{11} + 280 q^{12} + 126 q^{13} + 256 q^{14} - 86 q^{15} + 274 q^{16} - 94 q^{17} - 496 q^{18} + 204 q^{19} + 64 q^{20} - 74 q^{21} - 314 q^{22} - 166 q^{23} + 166 q^{24} - 1244 q^{25} + 832 q^{27} - 272 q^{28} + 134 q^{29} - 608 q^{30} + 310 q^{31} + 562 q^{32} - 428 q^{33} + 2385 q^{34} + 932 q^{35} + 418 q^{36} + 580 q^{37} + 1918 q^{38} + 1074 q^{39} + 5688 q^{40} + 2660 q^{41} + 3052 q^{42} + 112 q^{43} - 3100 q^{44} + 38 q^{45} - 3864 q^{46} - 3786 q^{47} - 7030 q^{48} - 5772 q^{49} - 9258 q^{50} - 3529 q^{51} - 11924 q^{52} - 6180 q^{53} - 6718 q^{54} - 8308 q^{55} - 7292 q^{56} + 1770 q^{57} - 856 q^{58} + 3524 q^{59} + 5160 q^{60} + 4570 q^{61} + 13400 q^{62} + 3850 q^{63} + 18660 q^{64} + 11646 q^{65} + 5116 q^{66} + 5848 q^{67} + 4309 q^{68} - 1846 q^{69} + 1884 q^{70} - 5304 q^{71} - 790 q^{72} - 332 q^{73} + 1872 q^{74} + 694 q^{75} - 1698 q^{76} - 562 q^{77} + 1948 q^{78} - 3750 q^{79} + 2728 q^{80} + 1102 q^{81} - 7748 q^{82} + 3818 q^{83} + 15084 q^{84} + 18150 q^{85} + 36002 q^{86} + 10738 q^{87} + 24882 q^{88} + 11016 q^{89} + 8920 q^{90} + 9596 q^{91} - 3196 q^{92} - 3318 q^{93} - 9168 q^{94} - 15280 q^{95} - 23776 q^{96} - 5972 q^{97} - 38172 q^{98} - 14306 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(153))\)

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
153.4.a \(\chi_{153}(1, \cdot)\) 153.4.a.a 1 1
153.4.a.b 1
153.4.a.c 1
153.4.a.d 1
153.4.a.e 2
153.4.a.f 3
153.4.a.g 3
153.4.a.h 4
153.4.a.i 4
153.4.d \(\chi_{153}(118, \cdot)\) 153.4.d.a 2 1
153.4.d.b 4
153.4.d.c 8
153.4.d.d 8
153.4.e \(\chi_{153}(52, \cdot)\) 153.4.e.a 44 2
153.4.e.b 52
153.4.f \(\chi_{153}(55, \cdot)\) 153.4.f.a 8 2
153.4.f.b 16
153.4.f.c 20
153.4.h \(\chi_{153}(16, \cdot)\) 153.4.h.a 104 2
153.4.l \(\chi_{153}(19, \cdot)\) 153.4.l.a 12 4
153.4.l.b 32
153.4.l.c 40
153.4.n \(\chi_{153}(4, \cdot)\) 153.4.n.a 208 4
153.4.o \(\chi_{153}(44, \cdot)\) 153.4.o.a 72 8
153.4.o.b 72
153.4.r \(\chi_{153}(25, \cdot)\) 153.4.r.a 416 8
153.4.s \(\chi_{153}(5, \cdot)\) 153.4.s.a 832 16

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(153))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(153)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)