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Properties

Label 171.4
Level 171
Weight 4
Dimension 2474
Nonzero newspaces 16
Newform subspaces 36
Sturm bound 8640
Trace bound 3

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Defining parameters

Level: \( N \) = \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 36 \)
Sturm bound: \(8640\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(171))\).

Total New Old
Modular forms 3384 2626 758
Cusp forms 3096 2474 622
Eisenstein series 288 152 136

Trace form

\( 2474 q - 21 q^{2} - 30 q^{3} - q^{4} + 3 q^{5} - 54 q^{6} - 53 q^{7} - 159 q^{8} - 126 q^{9} + O(q^{10}) \) \( 2474 q - 21 q^{2} - 30 q^{3} - q^{4} + 3 q^{5} - 54 q^{6} - 53 q^{7} - 159 q^{8} - 126 q^{9} - 105 q^{10} + 105 q^{11} + 276 q^{12} - 53 q^{13} + 57 q^{14} - 90 q^{15} + 263 q^{16} - 279 q^{17} - 468 q^{18} + 395 q^{19} + 498 q^{20} - 78 q^{21} + 69 q^{22} + 21 q^{23} + 162 q^{24} - 451 q^{25} + 345 q^{26} + 828 q^{27} - 2720 q^{28} - 759 q^{29} - 612 q^{30} - 647 q^{31} - 558 q^{32} - 432 q^{33} + 1692 q^{34} + 1077 q^{35} + 558 q^{36} + 556 q^{37} + 1743 q^{38} - 1590 q^{39} + 2382 q^{40} + 687 q^{41} + 936 q^{42} + 2575 q^{43} + 8772 q^{44} + 5418 q^{45} + 5232 q^{46} + 2571 q^{47} + 2022 q^{48} - 2877 q^{49} - 7122 q^{50} - 2970 q^{51} - 9815 q^{52} - 4995 q^{53} - 7866 q^{54} - 8421 q^{55} - 18012 q^{56} - 3855 q^{57} - 6006 q^{58} - 5181 q^{59} - 9468 q^{60} - 7451 q^{61} - 9510 q^{62} - 2250 q^{63} - 253 q^{64} + 573 q^{65} + 6840 q^{66} + 7327 q^{67} + 16920 q^{68} + 3582 q^{69} + 19077 q^{70} + 8955 q^{71} + 8118 q^{72} + 6892 q^{73} + 7077 q^{74} + 690 q^{75} + 5642 q^{76} + 4278 q^{77} + 1944 q^{78} - 737 q^{79} - 987 q^{80} + 1098 q^{81} - 5118 q^{82} + 1257 q^{83} - 1320 q^{84} + 225 q^{85} - 1374 q^{86} + 270 q^{87} + 1263 q^{88} - 2493 q^{89} + 3726 q^{90} + 875 q^{91} - 4272 q^{92} + 390 q^{93} + 20544 q^{94} + 27111 q^{95} + 25560 q^{96} + 23653 q^{97} + 45288 q^{98} + 11592 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(171))\)

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
171.4.a \(\chi_{171}(1, \cdot)\) 171.4.a.a 1 1
171.4.a.b 1
171.4.a.c 1
171.4.a.d 1
171.4.a.e 2
171.4.a.f 3
171.4.a.g 3
171.4.a.h 4
171.4.a.i 6
171.4.d \(\chi_{171}(170, \cdot)\) 171.4.d.a 4 1
171.4.d.b 16
171.4.e \(\chi_{171}(58, \cdot)\) 171.4.e.a 54 2
171.4.e.b 54
171.4.f \(\chi_{171}(64, \cdot)\) 171.4.f.a 2 2
171.4.f.b 2
171.4.f.c 4
171.4.f.d 4
171.4.f.e 4
171.4.f.f 10
171.4.f.g 10
171.4.f.h 12
171.4.g \(\chi_{171}(106, \cdot)\) 171.4.g.a 116 2
171.4.h \(\chi_{171}(7, \cdot)\) 171.4.h.a 116 2
171.4.k \(\chi_{171}(50, \cdot)\) 171.4.k.a 116 2
171.4.l \(\chi_{171}(56, \cdot)\) 171.4.l.a 116 2
171.4.m \(\chi_{171}(8, \cdot)\) 171.4.m.a 40 2
171.4.t \(\chi_{171}(122, \cdot)\) 171.4.t.a 116 2
171.4.u \(\chi_{171}(28, \cdot)\) 171.4.u.a 24 6
171.4.u.b 24
171.4.u.c 36
171.4.u.d 60
171.4.v \(\chi_{171}(25, \cdot)\) 171.4.v.a 348 6
171.4.w \(\chi_{171}(4, \cdot)\) 171.4.w.a 348 6
171.4.x \(\chi_{171}(14, \cdot)\) 171.4.x.a 348 6
171.4.y \(\chi_{171}(53, \cdot)\) 171.4.y.a 120 6
171.4.bd \(\chi_{171}(2, \cdot)\) 171.4.bd.a 348 6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(171))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(171)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 1}\)