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Properties

Label 1380.2.bv
Level $1380$
Weight $2$
Character orbit 1380.bv
Rep. character $\chi_{1380}(83,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $5600$
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.bv (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1380 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

Total New Old
Modular forms 5920 5920 0
Cusp forms 5600 5600 0
Eisenstein series 320 320 0

Trace form

\( 5600 q - 36 q^{6} + O(q^{10}) \) \( 5600 q - 36 q^{6} - 44 q^{10} - 6 q^{12} - 72 q^{13} - 80 q^{16} - 10 q^{18} - 88 q^{21} - 72 q^{25} - 44 q^{28} - 22 q^{30} - 44 q^{33} - 68 q^{36} - 88 q^{37} - 44 q^{40} - 22 q^{42} - 56 q^{46} + 22 q^{48} + 112 q^{52} - 44 q^{57} - 52 q^{58} - 22 q^{60} - 176 q^{61} - 44 q^{66} - 80 q^{70} + 14 q^{72} - 72 q^{73} - 88 q^{76} - 42 q^{78} + 8 q^{81} - 12 q^{82} - 72 q^{85} - 44 q^{88} - 440 q^{90} - 152 q^{93} - 36 q^{96} - 88 q^{97} + O(q^{100}) \)

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.