Properties

Label 1380.2.ba
Level $1380$
Weight $2$
Character orbit 1380.ba
Rep. character $\chi_{1380}(59,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2800$
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.ba (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1380 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2960 2960 0
Cusp forms 2800 2800 0
Eisenstein series 160 160 0

Trace form

\( 2800q - 32q^{4} - 26q^{6} - 36q^{9} + O(q^{10}) \) \( 2800q - 32q^{4} - 26q^{6} - 36q^{9} - 10q^{10} - 32q^{16} - 4q^{21} - 52q^{24} - 36q^{25} - 17q^{30} - 62q^{34} - 2q^{36} - 34q^{40} - 84q^{45} - 40q^{46} - 304q^{49} + 26q^{54} + 13q^{60} - 104q^{61} - 8q^{64} - 40q^{66} - 72q^{69} - 36q^{70} - 92q^{76} + 68q^{81} + 38q^{84} + 20q^{85} + 198q^{90} - 4q^{94} - 372q^{96} + O(q^{100}) \)

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

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