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Properties

Label 1380.4.bv
Level $1380$
Weight $4$
Character orbit 1380.bv
Rep. character $\chi_{1380}(83,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $17120$
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.bv (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1380 \)
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 17440 0
Cusp forms 17120 17120 0
Eisenstein series 320 320 0

Trace form

\( 17120 q - 36 q^{6} + O(q^{10}) \) \( 17120 q - 36 q^{6} - 44 q^{10} + 90 q^{12} - 72 q^{13} - 336 q^{16} + 14 q^{18} - 88 q^{21} - 72 q^{25} - 44 q^{28} - 22 q^{30} - 44 q^{33} - 548 q^{36} - 88 q^{37} - 44 q^{40} - 22 q^{42} - 488 q^{46} - 2570 q^{48} - 1088 q^{52} - 44 q^{57} - 1988 q^{58} - 22 q^{60} - 176 q^{61} - 44 q^{66} + 960 q^{70} + 2030 q^{72} - 72 q^{73} - 88 q^{76} - 1314 q^{78} - 6232 q^{81} + 3380 q^{82} - 72 q^{85} - 44 q^{88} + 37180 q^{90} - 5240 q^{93} - 36 q^{96} - 88 q^{97} + O(q^{100}) \)

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.