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Properties

Label 2678.2.bk
Level $2678$
Weight $2$
Character orbit 2678.bk
Rep. character $\chi_{2678}(107,\cdot)$
Character field $\Q(\zeta_{51})$
Dimension $3904$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.bk (of order \(51\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{51})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 11776 3904 7872
Cusp forms 11520 3904 7616
Eisenstein series 256 0 256

Trace form

\( 3904 q + 2 q^{3} - 244 q^{4} + 12 q^{7} + 116 q^{9} + O(q^{10}) \) \( 3904 q + 2 q^{3} - 244 q^{4} + 12 q^{7} + 116 q^{9} + 4 q^{10} - 4 q^{11} + 2 q^{12} - 30 q^{13} - 4 q^{14} - 4 q^{15} - 244 q^{16} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 4 q^{22} - 8 q^{23} + 130 q^{25} - 10 q^{26} - 16 q^{27} + 12 q^{28} - 8 q^{29} - 40 q^{31} - 8 q^{33} + 10 q^{35} + 184 q^{36} - 2 q^{37} + 2 q^{38} + 134 q^{39} + 4 q^{40} + 16 q^{41} + 8 q^{42} + 10 q^{43} - 4 q^{44} - 2 q^{47} + 2 q^{48} - 228 q^{49} + 20 q^{51} - 30 q^{52} + 14 q^{53} - 48 q^{54} + 20 q^{55} - 4 q^{56} - 4 q^{57} - 36 q^{58} + 10 q^{59} - 4 q^{60} - 2 q^{61} - 44 q^{62} + 2 q^{63} - 244 q^{64} + 68 q^{65} - 88 q^{66} + 10 q^{67} - 4 q^{68} + 304 q^{69} + 8 q^{70} + 488 q^{71} + 116 q^{73} + 38 q^{74} - 76 q^{75} + 10 q^{76} + 142 q^{77} + 52 q^{78} - 60 q^{79} + 98 q^{81} + 8 q^{82} - 10 q^{83} + 16 q^{84} + 64 q^{85} - 82 q^{86} - 16 q^{87} + 4 q^{88} - 8 q^{89} - 44 q^{90} - 236 q^{91} - 8 q^{92} - 264 q^{93} - 26 q^{94} + 4 q^{95} - 384 q^{97} + 56 q^{98} - 356 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2678, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1339, [\chi])\)\(^{\oplus 2}\)