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Properties

Label 177.14
Level 177
Weight 14
Dimension 11246
Nonzero newspaces 4
Sturm bound 32480
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(32480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(177))\).

Total New Old
Modular forms 15196 11362 3834
Cusp forms 14964 11246 3718
Eisenstein series 232 116 116

Trace form

\( 11246 q + 132 q^{2} - 1487 q^{3} - 24994 q^{4} - 21012 q^{5} + 61207 q^{6} - 428218 q^{7} + 3661104 q^{8} - 3188675 q^{9} + O(q^{10}) \) \( 11246 q + 132 q^{2} - 1487 q^{3} - 24994 q^{4} - 21012 q^{5} + 61207 q^{6} - 428218 q^{7} + 3661104 q^{8} - 3188675 q^{9} - 7599586 q^{10} + 21021000 q^{11} - 41646341 q^{12} - 51164494 q^{13} + 249482784 q^{14} - 103410137 q^{15} - 150215770 q^{16} + 67312116 q^{17} + 70150183 q^{18} - 84464386 q^{19} - 831639408 q^{20} + 373387939 q^{21} + 2362841654 q^{22} - 3380274960 q^{23} + 3237214867 q^{24} + 2679774380 q^{25} - 5229401352 q^{26} - 774841007 q^{27} - 9013679098 q^{28} + 11961751164 q^{29} - 4482947621 q^{30} - 353597866 q^{31} + 19329359040 q^{32} - 17285050757 q^{33} - 3464285170 q^{34} + 46416192000 q^{35} - 13252012805 q^{36} - 43826005438 q^{37} - 45682094832 q^{38} - 13826199449 q^{39} + 62268351206 q^{40} - 21160572828 q^{41} + 173646750211 q^{42} + 8398970894 q^{43} - 333920969184 q^{44} - 113997401892 q^{45} + 381379090342 q^{46} + 1134368153066 q^{47} - 1436927267645 q^{48} - 2346815482844 q^{49} - 267519135556 q^{50} + 1885030433811 q^{51} + 3954478607766 q^{52} + 437169253024 q^{53} - 4696120399209 q^{54} - 4701111676876 q^{55} - 1736798035328 q^{56} + 2559963926684 q^{57} + 3697575028280 q^{58} + 4205526809272 q^{59} - 1730428094122 q^{60} - 5013313751834 q^{61} - 9339530959616 q^{62} - 5194688747284 q^{63} + 10806955660102 q^{64} + 12103392660438 q^{65} + 19798888967379 q^{66} + 4254865940242 q^{67} - 19970485757008 q^{68} - 16744599638937 q^{69} - 18060226833786 q^{70} + 9267164822116 q^{71} + 44790744771091 q^{72} + 2474995548804 q^{73} - 48390065360168 q^{74} + 17083324897242 q^{75} - 5766888774490 q^{76} - 3695987708160 q^{77} - 4093905678725 q^{78} + 3572892259382 q^{79} + 9411359483712 q^{80} - 1694577218915 q^{81} - 6239046035218 q^{82} + 6900537556536 q^{83} - 12088009681373 q^{84} - 11174573203042 q^{85} + 21648202598640 q^{86} + 5068117469527 q^{87} + 14865070169606 q^{88} - 11011579222428 q^{89} - 4038700759877 q^{90} + 18596072577734 q^{91} - 18419262671040 q^{92} + 17702893407571 q^{93} - 53394282181498 q^{94} - 30330049072368 q^{95} + 7210670010019 q^{96} + 48180366643898 q^{97} - 286826028671370 q^{98} + 11171421260971 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(177))\)

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
177.14.a \(\chi_{177}(1, \cdot)\) 177.14.a.a 30 1
177.14.a.b 31
177.14.a.c 31
177.14.a.d 32
177.14.d \(\chi_{177}(176, \cdot)\) n/a 258 1
177.14.e \(\chi_{177}(4, \cdot)\) n/a 3640 28
177.14.f \(\chi_{177}(2, \cdot)\) n/a 7224 28

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)