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Properties

Label 2678.2.bf
Level $2678$
Weight $2$
Character orbit 2678.bf
Rep. character $\chi_{2678}(285,\cdot)$
Character field $\Q(\zeta_{34})$
Dimension $1984$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.bf (of order \(34\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{34})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 5888 1984 3904
Cusp forms 5760 1984 3776
Eisenstein series 128 0 128

Trace form

\( 1984 q + 4 q^{3} + 124 q^{4} - 116 q^{9} + O(q^{10}) \) \( 1984 q + 4 q^{3} + 124 q^{4} - 116 q^{9} - 4 q^{10} - 4 q^{12} - 4 q^{13} + 8 q^{14} - 124 q^{16} - 8 q^{17} + 4 q^{22} + 124 q^{25} + 16 q^{27} - 16 q^{29} + 252 q^{36} + 8 q^{38} + 48 q^{39} + 4 q^{40} + 8 q^{42} - 4 q^{43} + 4 q^{48} + 116 q^{49} - 24 q^{51} + 4 q^{52} - 4 q^{53} + 24 q^{55} - 8 q^{56} + 56 q^{61} + 8 q^{62} + 124 q^{64} - 28 q^{65} + 152 q^{66} + 8 q^{68} - 200 q^{69} - 4 q^{74} - 12 q^{75} + 248 q^{77} + 8 q^{78} - 16 q^{79} - 172 q^{81} + 8 q^{82} - 24 q^{87} - 4 q^{88} + 36 q^{90} - 214 q^{91} + 68 q^{94} + 40 q^{95} + O(q^{100}) \)

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

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