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Properties

Label 3900.2.fk
Level $3900$
Weight $2$
Character orbit 3900.fk
Rep. character $\chi_{3900}(113,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2240$
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.fk (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 975 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 13632 2240 11392
Cusp forms 13248 2240 11008
Eisenstein series 384 0 384

Trace form

\( 2240 q + O(q^{10}) \) \( 2240 q - 40 q^{19} - 24 q^{27} + 8 q^{33} + 8 q^{37} + 40 q^{39} - 4 q^{43} + 10 q^{45} - 8 q^{55} - 24 q^{57} - 86 q^{63} - 40 q^{67} - 70 q^{69} + 80 q^{73} + 66 q^{75} + 56 q^{85} + 96 q^{87} - 16 q^{93} + 76 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1950, [\chi])\)\(^{\oplus 2}\)