Properties

Label 1380.2.q
Level $1380$
Weight $2$
Character orbit 1380.q
Rep. character $\chi_{1380}(827,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $560$
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.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1380 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 592 592 0
Cusp forms 560 560 0
Eisenstein series 32 32 0

Trace form

\( 560q - 8q^{6} + O(q^{10}) \) \( 560q - 8q^{6} - 16q^{12} - 16q^{13} - 8q^{16} - 12q^{18} - 16q^{25} + 24q^{36} - 32q^{46} - 44q^{48} + 64q^{52} + 8q^{58} - 8q^{70} - 36q^{72} - 16q^{73} + 20q^{78} - 96q^{81} - 32q^{82} - 16q^{85} + 64q^{93} - 8q^{96} + O(q^{100}) \)

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

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