Properties

Label 1380.2.bs
Level $1380$
Weight $2$
Character orbit 1380.bs
Rep. character $\chi_{1380}(37,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $480$
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.bs (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
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 6000 480 5520
Cusp forms 5520 480 5040
Eisenstein series 480 0 480

Trace form

\( 480q + O(q^{10}) \) \( 480q + 8q^{13} - 72q^{23} + 8q^{25} - 8q^{31} - 8q^{35} + 88q^{37} + 24q^{41} + 168q^{47} + 32q^{55} + 88q^{57} - 88q^{61} + 24q^{71} - 8q^{73} - 32q^{75} - 40q^{77} + 48q^{81} + 64q^{85} + 40q^{87} + 220q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)