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Properties

Label 2678.2.f
Level $2678$
Weight $2$
Character orbit 2678.f
Rep. character $\chi_{2678}(159,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $244$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2678, [\chi])\).

Total New Old
Modular forms 736 244 492
Cusp forms 720 244 476
Eisenstein series 16 0 16

Trace form

\( 244 q - 2 q^{3} + 244 q^{4} - 12 q^{7} - 116 q^{9} + O(q^{10}) \) \( 244 q - 2 q^{3} + 244 q^{4} - 12 q^{7} - 116 q^{9} - 4 q^{10} + 4 q^{11} - 2 q^{12} + 30 q^{13} + 4 q^{14} + 4 q^{15} + 244 q^{16} + 4 q^{17} - 10 q^{19} + 18 q^{21} - 4 q^{22} + 8 q^{23} - 130 q^{25} + 10 q^{26} + 16 q^{27} - 12 q^{28} + 8 q^{29} + 40 q^{31} + 8 q^{33} - 10 q^{35} - 116 q^{36} + 2 q^{37} - 2 q^{38} + 2 q^{39} - 4 q^{40} - 16 q^{41} - 8 q^{42} - 10 q^{43} + 4 q^{44} + 2 q^{47} - 2 q^{48} + 228 q^{49} - 20 q^{51} + 30 q^{52} - 14 q^{53} + 48 q^{54} - 20 q^{55} + 4 q^{56} + 4 q^{57} + 36 q^{58} - 10 q^{59} + 4 q^{60} + 2 q^{61} + 44 q^{62} - 2 q^{63} + 244 q^{64} - 68 q^{65} - 48 q^{66} - 10 q^{67} + 4 q^{68} - 32 q^{69} - 8 q^{70} + 56 q^{71} - 116 q^{73} - 38 q^{74} + 76 q^{75} - 10 q^{76} - 6 q^{77} - 52 q^{78} + 60 q^{79} - 98 q^{81} - 8 q^{82} + 10 q^{83} + 18 q^{84} + 4 q^{85} + 14 q^{86} + 16 q^{87} - 4 q^{88} + 8 q^{89} + 44 q^{90} + 32 q^{91} + 8 q^{92} - 8 q^{93} - 42 q^{94} - 4 q^{95} + 10 q^{97} + 80 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2678, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2678, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2678, [\chi]) \cong \)