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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

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

Display 100 coefficients 10 coefficients

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 available 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

\( S_{3}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 1}\)