Properties

Label 2678.2.bb
Level $2678$
Weight $2$
Character orbit 2678.bb
Rep. character $\chi_{2678}(617,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $480$
Sturm bound $728$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.bb (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

\( 480 q + 8 q^{7} + 232 q^{9} + O(q^{10}) \) \( 480 q + 8 q^{7} + 232 q^{9} - 24 q^{13} - 16 q^{15} + 240 q^{16} + 24 q^{17} + 24 q^{23} - 8 q^{26} + 8 q^{28} + 16 q^{29} + 16 q^{33} - 48 q^{36} - 16 q^{41} - 24 q^{46} + 48 q^{49} - 8 q^{52} - 16 q^{55} - 24 q^{56} + 24 q^{58} + 40 q^{59} - 32 q^{60} + 120 q^{63} + 64 q^{66} + 80 q^{79} - 224 q^{81} - 56 q^{83} - 16 q^{91} - 16 q^{92} - 136 q^{93} + 72 q^{97} + 64 q^{98} + O(q^{100}) \)

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

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