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Properties

Label 3900.2.fw
Level $3900$
Weight $2$
Character orbit 3900.fw
Rep. character $\chi_{3900}(127,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $6720$
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.fw (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1300 \)
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 13568 6720 6848
Cusp forms 13312 6720 6592
Eisenstein series 256 0 256

Trace form

\( 6720 q + O(q^{10}) \) \( 6720 q + 8 q^{10} - 16 q^{12} + 4 q^{13} - 20 q^{17} - 28 q^{22} - 40 q^{25} - 8 q^{30} - 60 q^{32} + 12 q^{37} - 104 q^{40} + 20 q^{42} - 12 q^{45} - 372 q^{50} + 124 q^{52} + 8 q^{53} + 72 q^{58} + 124 q^{62} - 40 q^{65} - 24 q^{78} - 840 q^{81} - 8 q^{82} + 104 q^{88} + 184 q^{92} - 40 q^{94} + O(q^{100}) \)

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

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