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Properties

Label 1077.2.e
Level $1077$
Weight $2$
Character orbit 1077.e
Rep. character $\chi_{1077}(4,\cdot)$
Character field $\Q(\zeta_{179})$
Dimension $10680$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1077 = 3 \cdot 359 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1077.e (of order \(179\) and degree \(178\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 359 \)
Character field: \(\Q(\zeta_{179})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1077, [\chi])\).

Total New Old
Modular forms 21716 10680 11036
Cusp forms 21004 10680 10324
Eisenstein series 712 0 712

Trace form

\( 10680 q - 4 q^{2} - 64 q^{4} - 4 q^{5} - 8 q^{7} - 24 q^{8} - 60 q^{9} + O(q^{10}) \) \( 10680 q - 4 q^{2} - 64 q^{4} - 4 q^{5} - 8 q^{7} - 24 q^{8} - 60 q^{9} - 20 q^{10} - 16 q^{11} - 8 q^{12} - 8 q^{13} - 24 q^{14} - 80 q^{16} - 20 q^{17} - 4 q^{18} - 12 q^{19} - 28 q^{20} - 4 q^{21} - 44 q^{22} - 32 q^{23} - 12 q^{24} - 72 q^{25} - 20 q^{26} - 72 q^{28} - 28 q^{29} - 16 q^{30} - 16 q^{31} - 72 q^{32} - 12 q^{34} - 56 q^{35} - 64 q^{36} - 40 q^{37} - 40 q^{38} - 8 q^{39} - 68 q^{40} - 20 q^{41} - 36 q^{42} - 48 q^{43} - 80 q^{44} - 4 q^{45} - 104 q^{46} - 64 q^{47} - 32 q^{48} - 80 q^{49} - 76 q^{50} - 16 q^{51} - 120 q^{52} - 60 q^{53} - 68 q^{55} - 168 q^{56} - 12 q^{57} - 96 q^{58} - 40 q^{59} - 44 q^{60} - 60 q^{61} - 104 q^{62} - 8 q^{63} - 176 q^{64} - 64 q^{65} - 32 q^{66} - 80 q^{67} - 164 q^{68} - 12 q^{69} - 176 q^{70} - 60 q^{71} - 24 q^{72} - 40 q^{73} - 132 q^{74} - 24 q^{75} - 124 q^{76} - 144 q^{77} - 48 q^{78} - 68 q^{79} - 228 q^{80} - 60 q^{81} - 140 q^{82} - 60 q^{83} - 36 q^{84} - 112 q^{85} - 200 q^{86} - 36 q^{87} - 256 q^{88} - 20 q^{89} - 20 q^{90} - 80 q^{91} - 200 q^{92} - 44 q^{93} - 108 q^{94} - 88 q^{95} - 44 q^{96} - 64 q^{97} - 152 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1077, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1077, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1077, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(359, [\chi])\)\(^{\oplus 2}\)