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Properties

Label 177.10
Level 177
Weight 10
Dimension 7768
Nonzero newspaces 4
Sturm bound 23200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(23200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(177))\).

Total New Old
Modular forms 10556 7884 2672
Cusp forms 10324 7768 2556
Eisenstein series 232 116 116

Trace form

\( 7768q + 36q^{2} - 29q^{3} - 1250q^{4} + 5688q^{5} - 8777q^{6} - 9354q^{7} + 44784q^{8} - 26273q^{9} + O(q^{10}) \) \( 7768q + 36q^{2} - 29q^{3} - 1250q^{4} + 5688q^{5} - 8777q^{6} - 9354q^{7} + 44784q^{8} - 26273q^{9} - 39586q^{10} - 45216q^{11} + 157435q^{12} + 240558q^{13} - 651168q^{14} + 34963q^{15} + 358822q^{16} + 342360q^{17} + 236167q^{18} - 1474266q^{19} + 1485072q^{20} - 2204525q^{21} - 654538q^{22} + 5465952q^{23} + 454867q^{24} - 322550q^{25} - 12033288q^{26} - 29q^{27} + 10456710q^{28} + 3900024q^{29} + 12124699q^{30} - 13403082q^{31} - 21750336q^{32} - 3184301q^{33} + 17843918q^{34} + 16158240q^{35} - 7820741q^{36} - 3749394q^{37} + 37517328q^{38} - 29603261q^{39} - 64289434q^{40} + 23153976q^{41} - 489917q^{42} + 55012326q^{43} + 5631264q^{44} + 412162383q^{45} - 1053900698q^{46} - 340437788q^{47} + 764283331q^{48} + 827646946q^{49} + 1101151324q^{50} - 29405637q^{51} - 1153041002q^{52} - 1163652472q^{53} - 1473624345q^{54} - 352859806q^{55} + 1783765376q^{56} + 1341847499q^{57} + 665521592q^{58} + 1279770008q^{59} + 1581280598q^{60} + 19777886q^{61} - 673277824q^{62} - 2388156115q^{63} - 7820150970q^{64} - 2445972432q^{65} - 420074301q^{66} + 657674750q^{67} + 5420824624q^{68} + 3545197587q^{69} + 5806858374q^{70} - 188278264q^{71} - 6067812653q^{72} - 2816864018q^{73} - 3181796584q^{74} + 4628641737q^{75} - 875804250q^{76} - 372560832q^{77} + 792656251q^{78} + 419759862q^{79} - 527963328q^{80} - 172186913q^{81} - 53044690q^{82} + 2041375968q^{83} - 290993501q^{84} - 570536842q^{85} + 519481584q^{86} - 1836275213q^{87} + 561432326q^{88} - 181747368q^{89} - 259343237q^{90} - 1927479962q^{91} + 857070144q^{92} + 1205229427q^{93} + 1211277830q^{94} + 1999325952q^{95} + 432920995q^{96} - 678946818q^{97} + 28080624918q^{98} - 296662205q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(177))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
177.10.a \(\chi_{177}(1, \cdot)\) 177.10.a.a 21 1
177.10.a.b 21
177.10.a.c 22
177.10.a.d 22
177.10.d \(\chi_{177}(176, \cdot)\) n/a 178 1
177.10.e \(\chi_{177}(4, \cdot)\) n/a 2520 28
177.10.f \(\chi_{177}(2, \cdot)\) n/a 4984 28

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)