Properties

Label 177.4.e
Level $177$
Weight $4$
Character orbit 177.e
Rep. character $\chi_{177}(4,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $840$
Newform subspaces $2$
Sturm bound $80$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.e (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(177, [\chi])\).

Total New Old
Modular forms 1736 840 896
Cusp forms 1624 840 784
Eisenstein series 112 0 112

Trace form

\( 840q - 120q^{4} + 12q^{6} + 12q^{7} + 84q^{8} - 270q^{9} + O(q^{10}) \) \( 840q - 120q^{4} + 12q^{6} + 12q^{7} + 84q^{8} - 270q^{9} + 100q^{10} + 96q^{11} + 24q^{12} + 68q^{13} + 140q^{14} - 84q^{15} - 440q^{16} + 40q^{17} - 96q^{19} - 428q^{20} - 496q^{22} + 64q^{23} + 144q^{24} - 370q^{25} - 172q^{26} + 320q^{28} - 104q^{29} + 48q^{30} + 288q^{31} + 812q^{32} + 96q^{33} + 48q^{34} + 400q^{35} - 1080q^{36} + 140q^{37} - 52q^{38} + 336q^{39} + 940q^{40} + 704q^{41} - 192q^{42} + 896q^{43} + 612q^{44} + 10780q^{46} + 4452q^{47} + 288q^{48} + 1510q^{49} + 1624q^{50} + 456q^{51} - 3336q^{52} - 2320q^{53} + 108q^{54} - 6764q^{55} - 25860q^{56} + 384q^{57} - 6852q^{58} - 6728q^{59} + 216q^{60} - 3900q^{61} - 3488q^{62} + 108q^{63} - 14268q^{64} - 1744q^{65} - 2136q^{66} + 888q^{67} + 5560q^{68} + 96q^{69} + 14964q^{70} + 14512q^{71} + 756q^{72} + 9100q^{73} + 23552q^{74} - 624q^{75} + 1472q^{76} + 24q^{77} + 1452q^{78} - 2340q^{79} - 4384q^{80} - 2430q^{81} + 2388q^{82} - 1248q^{83} - 456q^{84} + 288q^{85} + 40q^{86} + 12q^{87} - 4188q^{88} - 3864q^{89} + 900q^{90} - 1080q^{91} + 5324q^{92} + 468q^{93} - 1056q^{94} - 4272q^{95} + 1644q^{96} + 1916q^{97} + 46334q^{98} + 864q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
177.4.e.a \(420\) \(10.443\) None \(-2\) \(45\) \(14\) \(6\)
177.4.e.b \(420\) \(10.443\) None \(2\) \(-45\) \(-14\) \(6\)

Decomposition of \(S_{4}^{\mathrm{old}}(177, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(177, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)