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Properties

Label 1380.4.bs
Level $1380$
Weight $4$
Character orbit 1380.bs
Rep. character $\chi_{1380}(37,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1440$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1380.bs (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1380, [\chi])\).

Total New Old
Modular forms 17520 1440 16080
Cusp forms 17040 1440 15600
Eisenstein series 480 0 480

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q - 96 q^{13} + 1704 q^{23} - 592 q^{25} + 256 q^{31} - 688 q^{35} + 2376 q^{37} - 528 q^{41} - 5904 q^{47} - 928 q^{55} + 7656 q^{57} + 1056 q^{61} + 432 q^{71} - 144 q^{73} + 1248 q^{75} - 2240 q^{77} + 11664 q^{81} + 1224 q^{85} - 960 q^{87} + 720 q^{93} - 2440 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

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