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Properties

Label 3900.2.bt
Level $3900$
Weight $2$
Character orbit 3900.bt
Rep. character $\chi_{3900}(251,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1040$
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.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 156 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 1728 1088 640
Cusp forms 1632 1040 592
Eisenstein series 96 48 48

Trace form

\( 1040 q + 2 q^{4} - 18 q^{6} + 2 q^{9} + O(q^{10}) \) \( 1040 q + 2 q^{4} - 18 q^{6} + 2 q^{9} + 16 q^{12} + 12 q^{13} - 10 q^{16} + 20 q^{22} + 54 q^{24} + 24 q^{28} + 6 q^{33} + 16 q^{36} + 36 q^{37} + 4 q^{42} - 48 q^{46} - 22 q^{48} - 456 q^{49} + 64 q^{52} - 54 q^{54} - 6 q^{58} + 92 q^{64} - 20 q^{66} + 46 q^{69} + 66 q^{72} - 12 q^{76} - 26 q^{78} - 14 q^{81} - 2 q^{82} + 42 q^{84} - 60 q^{88} + 48 q^{93} + 12 q^{94} - 24 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)