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Properties

Label 155.4
Level 155
Weight 4
Dimension 2548
Nonzero newspaces 12
Newform subspaces 22
Sturm bound 7680
Trace bound 2

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Defining parameters

Level: \( N \) = \( 155 = 5 \cdot 31 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 22 \)
Sturm bound: \(7680\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(155))\).

Total New Old
Modular forms 3000 2724 276
Cusp forms 2760 2548 212
Eisenstein series 240 176 64

Trace form

\( 2548 q - 22 q^{2} - 34 q^{3} - 46 q^{4} - 35 q^{5} - 74 q^{6} - 42 q^{7} - 30 q^{8} + 16 q^{9} + O(q^{10}) \) \( 2548 q - 22 q^{2} - 34 q^{3} - 46 q^{4} - 35 q^{5} - 74 q^{6} - 42 q^{7} - 30 q^{8} + 16 q^{9} - 85 q^{10} - 154 q^{11} - 62 q^{12} + 46 q^{13} + 18 q^{14} - 25 q^{15} + 38 q^{16} - 82 q^{17} - 214 q^{18} - 230 q^{19} + 35 q^{20} + 486 q^{21} + 2746 q^{22} + 906 q^{23} + 1410 q^{24} - 95 q^{25} - 994 q^{26} - 1450 q^{27} - 3966 q^{28} - 1610 q^{29} - 1910 q^{30} - 1782 q^{31} - 5612 q^{32} - 1598 q^{33} - 1982 q^{34} - 285 q^{35} + 278 q^{36} + 518 q^{37} + 2330 q^{38} + 3062 q^{39} + 3555 q^{40} + 2266 q^{41} + 6186 q^{42} + 346 q^{43} - 542 q^{44} - 275 q^{45} - 714 q^{46} + 998 q^{47} + 11116 q^{48} + 6284 q^{49} + 5480 q^{50} + 8626 q^{51} + 4928 q^{52} + 626 q^{53} - 2480 q^{54} - 865 q^{55} - 8460 q^{56} - 7810 q^{57} - 10720 q^{58} - 4330 q^{59} - 13040 q^{60} - 10004 q^{61} - 11442 q^{62} - 13944 q^{63} - 8666 q^{64} - 4835 q^{65} - 18028 q^{66} - 2142 q^{67} - 4436 q^{68} - 618 q^{69} + 1200 q^{70} + 2566 q^{71} + 16140 q^{72} + 5986 q^{73} + 16348 q^{74} + 13955 q^{75} + 38660 q^{76} + 23646 q^{77} + 39592 q^{78} + 5070 q^{79} + 8915 q^{80} + 3868 q^{81} + 2306 q^{82} - 1014 q^{83} - 7422 q^{84} - 1945 q^{85} - 8554 q^{86} - 7270 q^{87} - 25950 q^{88} - 11730 q^{89} - 14200 q^{90} - 11334 q^{91} - 31872 q^{92} - 21894 q^{93} - 14972 q^{94} - 9365 q^{95} - 29104 q^{96} - 10162 q^{97} - 24806 q^{98} - 6058 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(155))\)

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
155.4.a \(\chi_{155}(1, \cdot)\) 155.4.a.a 1 1
155.4.a.b 4
155.4.a.c 6
155.4.a.d 9
155.4.a.e 10
155.4.b \(\chi_{155}(94, \cdot)\) 155.4.b.a 20 1
155.4.b.b 26
155.4.e \(\chi_{155}(36, \cdot)\) 155.4.e.a 32 2
155.4.e.b 32
155.4.f \(\chi_{155}(92, \cdot)\) 155.4.f.a 4 2
155.4.f.b 8
155.4.f.c 80
155.4.h \(\chi_{155}(16, \cdot)\) 155.4.h.a 64 4
155.4.h.b 64
155.4.j \(\chi_{155}(129, \cdot)\) 155.4.j.a 92 2
155.4.n \(\chi_{155}(4, \cdot)\) 155.4.n.a 184 4
155.4.p \(\chi_{155}(37, \cdot)\) 155.4.p.a 184 4
155.4.q \(\chi_{155}(41, \cdot)\) 155.4.q.a 128 8
155.4.q.b 128
155.4.r \(\chi_{155}(23, \cdot)\) 155.4.r.a 368 8
155.4.u \(\chi_{155}(9, \cdot)\) 155.4.u.a 368 8
155.4.x \(\chi_{155}(3, \cdot)\) 155.4.x.a 736 16

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(155))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(155)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)