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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
177.4.e.a 177.e 59.c $420$ $10.443$ None \(-2\) \(45\) \(14\) \(6\) $\mathrm{SU}(2)[C_{29}]$
177.4.e.b 177.e 59.c $420$ $10.443$ None \(2\) \(-45\) \(-14\) \(6\) $\mathrm{SU}(2)[C_{29}]$

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

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