Properties

Label 177.14.a
Level $177$
Weight $14$
Character orbit 177.a
Rep. character $\chi_{177}(1,\cdot)$
Character field $\Q$
Dimension $124$
Newform subspaces $4$
Sturm bound $280$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(280\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(177))\).

Total New Old
Modular forms 262 124 138
Cusp forms 258 124 134
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(31\)
\(+\)\(-\)\(-\)\(32\)
\(-\)\(+\)\(-\)\(31\)
\(-\)\(-\)\(+\)\(30\)
Plus space\(+\)\(61\)
Minus space\(-\)\(63\)

Trace form

\( 124q + 132q^{2} - 1458q^{3} + 507544q^{4} - 21012q^{5} + 154548q^{6} - 265196q^{7} + 1507356q^{8} + 65898684q^{9} + O(q^{10}) \) \( 124q + 132q^{2} - 1458q^{3} + 507544q^{4} - 21012q^{5} + 154548q^{6} - 265196q^{7} + 1507356q^{8} + 65898684q^{9} + 1585636q^{10} + 8331348q^{11} - 17915904q^{12} - 15690604q^{13} + 85177876q^{14} - 67400424q^{15} + 1975095544q^{16} + 207261380q^{17} + 70150212q^{18} - 582185340q^{19} + 128679644q^{20} + 373387968q^{21} + 1873980296q^{22} - 2974336960q^{23} + 4383832752q^{24} + 30431381868q^{25} - 7011075020q^{26} - 774840978q^{27} - 4010159760q^{28} + 15183992408q^{29} - 2183874048q^{30} + 1307240580q^{31} + 24315968404q^{32} - 261186120q^{33} + 40128666152q^{34} + 48440647328q^{35} + 269729690904q^{36} - 43733062676q^{37} - 12541875452q^{38} + 45566923572q^{39} + 63159400628q^{40} - 56207284880q^{41} + 190101015072q^{42} + 20353029536q^{43} - 228423897060q^{44} - 11166638292q^{45} + 156259433132q^{46} + 97823826260q^{47} - 171228266496q^{48} + 1560002781992q^{49} - 373885245932q^{50} - 302930937396q^{51} + 416338348360q^{52} + 938436255116q^{53} + 82133143668q^{54} - 544809161828q^{55} - 506506215356q^{56} - 925685844624q^{57} - 507617067708q^{58} - 391524455736q^{60} + 973911346728q^{61} - 2930701240824q^{62} - 140936027436q^{63} + 5013316236220q^{64} - 2294136779036q^{65} + 701696506392q^{66} - 589163284976q^{67} - 4907365667048q^{68} + 318688015788q^{69} + 6859346375756q^{70} + 2620934245404q^{71} + 801070779996q^{72} - 53829728088q^{73} + 2811696607472q^{74} - 2147148262926q^{75} - 16453396382368q^{76} - 6285262337268q^{77} - 5060213908164q^{78} + 1863871410320q^{79} + 8673223258336q^{80} + 35021262523644q^{81} + 2371808562900q^{82} + 12561134270988q^{83} - 6950145139704q^{84} + 9346656464156q^{85} + 1058885955272q^{86} + 2287497134808q^{87} - 9120342474180q^{88} - 14040462462144q^{89} + 842671981476q^{90} - 15771815917416q^{91} + 7477229231380q^{92} + 26140674919644q^{93} - 45431918285808q^{94} - 17449530093156q^{95} + 35737085113812q^{96} + 44683786448876q^{97} + 65370990929896q^{98} + 4427619912468q^{99} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 59
177.14.a.a \(30\) \(189.799\) None \(-138\) \(21870\) \(-137742\) \(-879443\) \(-\) \(-\)
177.14.a.b \(31\) \(189.799\) None \(-52\) \(-22599\) \(33486\) \(-1135539\) \(+\) \(+\)
177.14.a.c \(31\) \(189.799\) None \(310\) \(22599\) \(81008\) \(1002941\) \(-\) \(+\)
177.14.a.d \(32\) \(189.799\) None \(12\) \(-23328\) \(2236\) \(746845\) \(+\) \(-\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(177)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)