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Properties

Label 2678.2.w
Level $2678$
Weight $2$
Character orbit 2678.w
Rep. character $\chi_{2678}(47,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $480$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 1472 480 992
Cusp forms 1440 480 960
Eisenstein series 32 0 32

Trace form

\( 480 q - 4 q^{7} - 464 q^{9} + O(q^{10}) \) \( 480 q - 4 q^{7} - 464 q^{9} - 24 q^{11} - 24 q^{13} + 8 q^{15} + 240 q^{16} + 24 q^{19} - 8 q^{26} - 4 q^{28} + 16 q^{29} - 8 q^{33} - 24 q^{35} + 8 q^{41} + 24 q^{44} + 12 q^{46} + 24 q^{47} - 8 q^{52} + 72 q^{53} + 32 q^{55} + 36 q^{57} + 12 q^{58} + 28 q^{59} - 8 q^{60} + 24 q^{63} + 96 q^{65} - 32 q^{66} + 48 q^{67} + 48 q^{70} + 24 q^{71} + 24 q^{74} + 48 q^{76} - 84 q^{78} + 80 q^{79} + 448 q^{81} - 68 q^{83} - 24 q^{85} + 12 q^{86} + 24 q^{87} + 8 q^{91} - 16 q^{92} - 88 q^{93} - 48 q^{97} + 16 q^{98} + 72 q^{99} + O(q^{100}) \)

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

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