Properties

Label 3900.2.ed
Level $3900$
Weight $2$
Character orbit 3900.ed
Rep. character $\chi_{3900}(619,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3360$
Sturm bound $1680$

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Defining parameters

Level: \( N \) \(=\) \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3900.ed (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1300 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3900, [\chi])\).

Total New Old
Modular forms 6784 3360 3424
Cusp forms 6656 3360 3296
Eisenstein series 128 0 128

Trace form

\( 3360 q + 4 q^{5} - 840 q^{9} + O(q^{10}) \) \( 3360 q + 4 q^{5} - 840 q^{9} - 24 q^{16} - 20 q^{20} + 200 q^{22} - 20 q^{37} + 32 q^{40} - 40 q^{41} + 4 q^{45} + 40 q^{46} + 124 q^{50} - 180 q^{52} + 40 q^{53} + 120 q^{58} + 4 q^{60} - 16 q^{61} + 20 q^{65} + 16 q^{66} - 8 q^{70} + 40 q^{76} - 36 q^{80} - 840 q^{81} + 20 q^{85} - 156 q^{89} - 24 q^{94} - 60 q^{96} - 280 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)