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Properties

Label 1380.4.bt
Level $1380$
Weight $4$
Character orbit 1380.bt
Rep. character $\chi_{1380}(127,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $8640$
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.bt (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
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 17440 8640 8800
Cusp forms 17120 8640 8480
Eisenstein series 320 0 320

Trace form

\( 8640 q + 24 q^{6} + O(q^{10}) \) \( 8640 q + 24 q^{6} + 264 q^{16} + 760 q^{20} + 520 q^{22} - 864 q^{28} - 680 q^{32} + 216 q^{36} + 3200 q^{40} + 1184 q^{41} - 5940 q^{42} - 2280 q^{46} - 1056 q^{48} - 6368 q^{50} - 3636 q^{52} - 672 q^{56} + 2016 q^{58} + 840 q^{60} - 3648 q^{61} + 3344 q^{62} - 2832 q^{70} + 3328 q^{76} + 7008 q^{77} - 6964 q^{80} + 69984 q^{81} + 9320 q^{82} - 21168 q^{85} - 5600 q^{86} + 2888 q^{92} - 1824 q^{93} + 7656 q^{96} + 5432 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)