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Properties

Label 3900.2.bc
Level $3900$
Weight $2$
Character orbit 3900.bc
Rep. character $\chi_{3900}(151,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $532$
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.bc (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
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 532 1196
Cusp forms 1632 532 1100
Eisenstein series 96 0 96

Trace form

\( 532 q - 532 q^{9} + O(q^{10}) \) \( 532 q - 532 q^{9} - 32 q^{14} - 8 q^{16} - 8 q^{21} + 48 q^{22} - 12 q^{24} - 20 q^{26} - 32 q^{28} + 60 q^{32} + 8 q^{34} + 4 q^{37} + 4 q^{41} + 24 q^{42} + 36 q^{44} - 16 q^{46} + 32 q^{48} + 56 q^{52} - 8 q^{53} - 24 q^{57} + 40 q^{58} + 24 q^{61} - 8 q^{66} + 24 q^{68} - 28 q^{73} - 24 q^{74} - 24 q^{76} + 44 q^{78} + 532 q^{81} - 48 q^{86} + 20 q^{89} - 48 q^{92} + 8 q^{93} - 80 q^{94} - 28 q^{97} + 72 q^{98} + O(q^{100}) \)

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

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