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Properties

Label 3900.2.y
Level $3900$
Weight $2$
Character orbit 3900.y
Rep. character $\chi_{3900}(2107,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $432$
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 1728 432 1296
Cusp forms 1632 432 1200
Eisenstein series 96 0 96

Trace form

\( 432 q - 16 q^{6} - 24 q^{8} + O(q^{10}) \) \( 432 q - 16 q^{6} - 24 q^{8} - 8 q^{12} - 16 q^{16} - 8 q^{22} - 8 q^{28} + 16 q^{33} + 16 q^{36} + 32 q^{38} + 80 q^{46} + 32 q^{48} + 8 q^{52} + 48 q^{56} - 88 q^{58} - 128 q^{61} - 96 q^{66} - 32 q^{68} - 24 q^{72} - 16 q^{73} - 96 q^{76} + 96 q^{77} - 432 q^{81} + 64 q^{82} - 48 q^{86} + 80 q^{88} + 80 q^{92} - 32 q^{93} - 64 q^{96} - 80 q^{97} - 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)