Properties

Label 3900.2.bh
Level $3900$
Weight $2$
Character orbit 3900.bh
Rep. character $\chi_{3900}(1507,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $504$
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.bh (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
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 504 1224
Cusp forms 1632 504 1128
Eisenstein series 96 0 96

Trace form

\( 504 q + O(q^{10}) \) \( 504 q - 8 q^{12} - 4 q^{13} + 64 q^{16} - 40 q^{17} - 32 q^{22} + 32 q^{26} + 40 q^{42} + 56 q^{52} - 8 q^{53} + 64 q^{56} - 32 q^{62} + 24 q^{78} - 504 q^{81} + 48 q^{82} - 56 q^{88} + 32 q^{92} + O(q^{100}) \)

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

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