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Properties

Label 177.8
Level 177
Weight 8
Dimension 6030
Nonzero newspaces 4
Sturm bound 18560
Trace bound 1

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Defining parameters

Level: \( N \) = \( 177 = 3 \cdot 59 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(18560\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(177))\).

Total New Old
Modular forms 8236 6146 2090
Cusp forms 8004 6030 1974
Eisenstein series 232 116 116

Trace form

\( 6030q - 12q^{2} + 25q^{3} + 126q^{4} - 780q^{5} + 295q^{6} + 70q^{7} + 2640q^{8} - 1487q^{9} + O(q^{10}) \) \( 6030q - 12q^{2} + 25q^{3} + 126q^{4} - 780q^{5} + 295q^{6} + 70q^{7} + 2640q^{8} - 1487q^{9} - 4738q^{10} + 1896q^{11} - 4997q^{12} + 10138q^{13} + 768q^{14} + 21031q^{15} - 7770q^{16} - 56772q^{17} - 8777q^{18} + 17182q^{19} + 71760q^{20} - 3485q^{21} + 11318q^{22} + 30576q^{23} - 71309q^{24} - 148008q^{25} + 61176q^{26} + 39337q^{27} - 11834q^{28} - 73020q^{29} + 126331q^{30} + 553558q^{31} - 384192q^{32} - 51221q^{33} - 340690q^{34} + 49920q^{35} + 134107q^{36} - 537110q^{37} + 103440q^{38} - 275321q^{39} + 1029542q^{40} + 1259436q^{41} - 20765q^{42} - 1371602q^{43} - 174432q^{44} + 9952812q^{45} - 5895930q^{46} - 10978046q^{47} - 22097213q^{48} - 1466136q^{49} + 16081708q^{50} + 17475507q^{51} + 34593174q^{52} + 15062984q^{53} + 11898111q^{54} - 3535972q^{55} - 48781312q^{56} - 24533044q^{57} - 23071112q^{58} - 22741672q^{59} - 48686506q^{60} - 6404050q^{61} + 9751808q^{62} + 23880968q^{63} + 116782918q^{64} + 57020166q^{65} + 59714235q^{66} + 25884482q^{67} + 19135600q^{68} - 18411993q^{69} - 88096250q^{70} - 75928492q^{71} - 98488781q^{72} - 19115508q^{73} + 58815416q^{74} + 66317622q^{75} - 1586138q^{76} - 121344q^{77} - 1651781q^{78} + 13827382q^{79} - 3007680q^{80} - 1062911q^{81} + 7556558q^{82} + 8753496q^{83} + 317923q^{84} - 22141138q^{85} - 8229264q^{86} + 1971511q^{87} - 2502778q^{88} + 17056620q^{89} - 3411749q^{90} - 652602q^{91} - 2812992q^{92} - 14947661q^{93} - 6999610q^{94} + 6723600q^{95} + 10373155q^{96} + 17653570q^{97} + 540474726q^{98} + 1382155q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(177))\)

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
177.8.a \(\chi_{177}(1, \cdot)\) 177.8.a.a 16 1
177.8.a.b 17
177.8.a.c 17
177.8.a.d 18
177.8.d \(\chi_{177}(176, \cdot)\) n/a 138 1
177.8.e \(\chi_{177}(4, \cdot)\) n/a 1960 28
177.8.f \(\chi_{177}(2, \cdot)\) n/a 3864 28

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(177))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(177)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)