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Properties

Label 2678.2.h
Level $2678$
Weight $2$
Character orbit 2678.h
Rep. character $\chi_{2678}(365,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $208$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 103 \)
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 736 208 528
Cusp forms 720 208 512
Eisenstein series 16 0 16

Trace form

\( 208 q + 8 q^{3} - 104 q^{4} + 12 q^{5} - 4 q^{7} + 224 q^{9} + O(q^{10}) \) \( 208 q + 8 q^{3} - 104 q^{4} + 12 q^{5} - 4 q^{7} + 224 q^{9} - 16 q^{10} + 4 q^{11} - 4 q^{12} + 8 q^{14} - 104 q^{16} + 8 q^{17} + 8 q^{19} + 12 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{23} - 80 q^{25} + 8 q^{27} - 4 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 16 q^{33} - 8 q^{35} - 112 q^{36} + 56 q^{37} - 4 q^{38} + 8 q^{40} + 20 q^{41} + 8 q^{42} + 16 q^{43} + 4 q^{44} + 24 q^{45} - 24 q^{46} + 8 q^{47} - 4 q^{48} - 136 q^{49} - 8 q^{51} - 16 q^{53} + 12 q^{54} + 4 q^{55} - 4 q^{56} + 4 q^{57} + 4 q^{59} - 64 q^{61} - 4 q^{62} - 36 q^{63} + 208 q^{64} + 8 q^{65} + 32 q^{66} + 20 q^{67} + 8 q^{68} + 96 q^{69} - 32 q^{70} - 16 q^{71} + 72 q^{73} + 24 q^{74} + 4 q^{75} - 16 q^{76} - 12 q^{77} + 4 q^{78} - 56 q^{79} - 24 q^{80} + 320 q^{81} - 20 q^{82} + 8 q^{83} + 12 q^{84} - 20 q^{85} + 8 q^{86} - 56 q^{87} - 12 q^{88} - 16 q^{89} - 224 q^{90} + 4 q^{92} + 72 q^{93} - 24 q^{94} + 96 q^{95} - 40 q^{97} + 40 q^{98} + 4 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2678, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(103, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(206, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1339, [\chi])\)\(^{\oplus 2}\)