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Properties

Label 2678.2.ba
Level $2678$
Weight $2$
Character orbit 2678.ba
Rep. character $\chi_{2678}(665,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $488$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.ba (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 488 984
Cusp forms 1440 488 952
Eisenstein series 32 0 32

Trace form

\( 488 q + 12 q^{7} + 248 q^{9} + O(q^{10}) \) \( 488 q + 12 q^{7} + 248 q^{9} + 12 q^{11} - 4 q^{12} - 36 q^{13} - 40 q^{15} - 488 q^{16} + 52 q^{19} + 8 q^{21} + 24 q^{23} + 24 q^{25} + 16 q^{26} + 12 q^{28} + 16 q^{29} + 8 q^{31} - 8 q^{33} - 12 q^{35} + 48 q^{36} + 4 q^{37} + 52 q^{39} - 16 q^{41} - 44 q^{43} + 36 q^{44} - 12 q^{46} + 12 q^{47} + 24 q^{51} + 24 q^{52} - 36 q^{53} + 32 q^{55} - 32 q^{57} - 36 q^{58} + 28 q^{59} - 32 q^{60} + 104 q^{63} - 32 q^{66} + 20 q^{67} + 120 q^{69} - 48 q^{70} + 72 q^{71} + 4 q^{73} + 12 q^{74} + 64 q^{75} + 32 q^{76} - 24 q^{78} - 16 q^{79} - 276 q^{81} - 32 q^{83} + 4 q^{84} + 48 q^{85} - 24 q^{87} - 12 q^{89} - 8 q^{91} + 8 q^{92} + 96 q^{93} - 60 q^{94} + 4 q^{97} - 80 q^{98} + 108 q^{99} + O(q^{100}) \)

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

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