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Properties

Label 3900.2.dk
Level $3900$
Weight $2$
Character orbit 3900.dk
Rep. character $\chi_{3900}(607,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1008$
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.dk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 3456 1008 2448
Cusp forms 3264 1008 2256
Eisenstein series 192 0 192

Trace form

\( 1008 q + O(q^{10}) \) \( 1008 q + 16 q^{12} - 4 q^{13} - 32 q^{16} + 20 q^{17} - 28 q^{22} + 32 q^{26} - 20 q^{32} - 4 q^{37} + 64 q^{41} - 20 q^{42} - 16 q^{52} + 8 q^{53} - 64 q^{56} - 24 q^{58} - 4 q^{62} + 104 q^{73} + 128 q^{76} - 24 q^{78} + 504 q^{81} - 32 q^{82} + 256 q^{86} - 32 q^{88} - 184 q^{92} + 40 q^{97} + 112 q^{98} + O(q^{100}) \)

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

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