Properties

Label 1380.2.bt
Level $1380$
Weight $2$
Character orbit 1380.bt
Rep. character $\chi_{1380}(127,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $2880$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.bt (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

Total New Old
Modular forms 5920 2880 3040
Cusp forms 5600 2880 2720
Eisenstein series 320 0 320

Trace form

\( 2880q + 8q^{6} + O(q^{10}) \) \( 2880q + 8q^{6} + 8q^{16} - 40q^{20} - 40q^{22} + 32q^{28} - 40q^{32} - 8q^{36} - 32q^{41} + 180q^{42} + 40q^{46} - 32q^{48} + 32q^{50} + 252q^{52} + 96q^{56} + 32q^{58} + 40q^{60} + 64q^{61} + 112q^{62} - 112q^{70} - 64q^{76} - 96q^{77} - 404q^{80} + 288q^{81} - 40q^{82} + 432q^{85} - 160q^{86} - 56q^{92} + 32q^{93} - 88q^{96} - 56q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)