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Properties

Label 1380.2.bb
Level $1380$
Weight $2$
Character orbit 1380.bb
Rep. character $\chi_{1380}(89,\cdot)$
Character field $\Q(\zeta_{22})$
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.bb (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
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 3000 480 2520
Cusp forms 2760 480 2280
Eisenstein series 240 0 240

Trace form

\( 480 q + O(q^{10}) \) \( 480 q - 11 q^{15} - 16 q^{31} - 24 q^{39} + 20 q^{49} + 14 q^{55} - 44 q^{61} + 126 q^{69} + 35 q^{75} + 44 q^{79} + 52 q^{81} - 10 q^{85} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)