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Properties

Label 1380.4.bu
Level $1380$
Weight $4$
Character orbit 1380.bu
Rep. character $\chi_{1380}(77,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $2880$
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.bu (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
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 2880 14640
Cusp forms 17040 2880 14160
Eisenstein series 480 0 480

Trace form

\( 2880 q + 8 q^{3} + O(q^{10}) \) \( 2880 q + 8 q^{3} - 96 q^{13} + 8 q^{15} - 480 q^{21} + 720 q^{25} + 296 q^{27} + 432 q^{31} - 1584 q^{33} + 2232 q^{37} - 1968 q^{43} - 32 q^{51} + 2208 q^{55} + 848 q^{57} - 720 q^{61} + 3864 q^{63} - 4416 q^{67} - 3600 q^{73} + 5332 q^{75} + 4984 q^{81} + 4752 q^{85} + 3928 q^{87} + 6816 q^{91} + 6376 q^{93} + 19584 q^{97} + O(q^{100}) \)

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

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