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Properties

Label 177.6.e
Level $177$
Weight $6$
Character orbit 177.e
Rep. character $\chi_{177}(4,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $1400$
Sturm bound $120$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.e (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Sturm bound: \(120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(177, [\chi])\).

Total New Old
Modular forms 2856 1400 1456
Cusp forms 2744 1400 1344
Eisenstein series 112 0 112

Trace form

\( 1400 q - 800 q^{4} - 72 q^{6} + 76 q^{7} - 492 q^{8} - 4050 q^{9} + O(q^{10}) \) \( 1400 q - 800 q^{4} - 72 q^{6} + 76 q^{7} - 492 q^{8} - 4050 q^{9} + 596 q^{10} - 396 q^{11} + 792 q^{12} - 272 q^{13} + 1676 q^{14} + 396 q^{15} - 8728 q^{16} + 2656 q^{17} + 3444 q^{19} + 9268 q^{20} + 6136 q^{22} + 400 q^{23} - 3456 q^{24} - 35590 q^{25} + 1700 q^{26} - 16240 q^{28} + 8764 q^{29} - 7704 q^{30} - 24612 q^{31} - 724 q^{32} + 9792 q^{33} + 7424 q^{34} + 4192 q^{35} - 64800 q^{36} - 24 q^{37} - 36340 q^{38} - 1008 q^{39} + 20076 q^{40} - 18868 q^{41} - 12672 q^{42} + 14056 q^{43} - 13692 q^{44} + 372292 q^{46} + 33966 q^{47} + 52704 q^{48} - 392018 q^{49} - 648824 q^{50} + 2448 q^{51} - 411576 q^{52} - 120292 q^{53} - 5832 q^{54} + 232010 q^{55} + 1225020 q^{56} - 14328 q^{57} + 568228 q^{58} + 401464 q^{59} - 30456 q^{60} + 250384 q^{61} - 49592 q^{62} + 6156 q^{63} - 974908 q^{64} - 443506 q^{65} + 25848 q^{66} - 532324 q^{67} - 1030760 q^{68} + 28044 q^{69} - 1199564 q^{70} - 251768 q^{71} - 39852 q^{72} + 304770 q^{73} + 1447928 q^{74} + 115488 q^{75} + 104320 q^{76} + 245388 q^{77} + 141948 q^{78} + 264080 q^{79} - 56224 q^{80} - 328050 q^{81} - 377580 q^{82} + 169068 q^{83} - 132552 q^{84} + 197300 q^{85} - 15320 q^{86} - 147492 q^{87} + 565764 q^{88} + 314988 q^{89} + 48276 q^{90} + 136008 q^{91} + 84140 q^{92} + 24516 q^{93} - 13488 q^{94} + 180708 q^{95} + 21996 q^{96} + 59200 q^{97} + 4791374 q^{98} - 32076 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(177, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(177, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)