Properties

Label 177.3
Level 177
Weight 3
Dimension 1682
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 6960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(6960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(177))\).

Total New Old
Modular forms 2436 1794 642
Cusp forms 2204 1682 522
Eisenstein series 232 112 120

Trace form

\( 1682q - 29q^{3} - 58q^{4} - 29q^{6} - 58q^{7} - 29q^{9} + O(q^{10}) \) \( 1682q - 29q^{3} - 58q^{4} - 29q^{6} - 58q^{7} - 29q^{9} - 58q^{10} - 29q^{12} - 58q^{13} - 29q^{15} - 58q^{16} - 29q^{18} - 58q^{19} - 29q^{21} - 58q^{22} - 29q^{24} - 58q^{25} - 29q^{27} - 58q^{28} - 29q^{30} - 58q^{31} - 29q^{33} - 58q^{34} - 29q^{36} - 58q^{37} - 29q^{39} - 58q^{40} - 29q^{42} - 58q^{43} - 406q^{45} - 1450q^{46} - 638q^{47} - 1769q^{48} - 1102q^{49} - 1856q^{50} - 841q^{51} - 1450q^{52} - 580q^{53} - 841q^{54} - 580q^{55} - 928q^{56} - 174q^{57} - 116q^{58} + 116q^{59} + 638q^{60} + 290q^{61} + 464q^{62} + 696q^{63} + 2726q^{64} + 1218q^{65} + 1595q^{66} + 986q^{67} + 2320q^{68} + 1247q^{69} + 2726q^{70} + 1508q^{71} + 2407q^{72} + 812q^{73} + 1856q^{74} + 464q^{75} - 58q^{76} - 29q^{78} - 58q^{79} - 29q^{81} - 58q^{82} - 29q^{84} - 58q^{85} - 29q^{87} - 58q^{88} - 29q^{90} - 58q^{91} - 29q^{93} - 58q^{94} - 29q^{96} - 58q^{97} - 3306q^{98} - 29q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(177))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
177.3.b \(\chi_{177}(119, \cdot)\) 177.3.b.a 38 1
177.3.c \(\chi_{177}(58, \cdot)\) 177.3.c.a 20 1
177.3.g \(\chi_{177}(10, \cdot)\) 177.3.g.a 560 28
177.3.h \(\chi_{177}(5, \cdot)\) 177.3.h.a 1064 28

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)