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Properties

Label 3900.2.ej
Level $3900$
Weight $2$
Character orbit 3900.ej
Rep. character $\chi_{3900}(547,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2880$
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.ej (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 6784 2880 3904
Cusp forms 6656 2880 3776
Eisenstein series 128 0 128

Trace form

\( 2880 q - 24 q^{8} + O(q^{10}) \) \( 2880 q - 24 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{22} - 8 q^{28} + 8 q^{30} + 16 q^{33} + 152 q^{38} - 8 q^{40} + 280 q^{44} + 32 q^{48} + 8 q^{52} + 192 q^{58} + 120 q^{64} - 32 q^{68} - 24 q^{70} - 24 q^{72} - 16 q^{73} + 96 q^{77} + 80 q^{80} + 720 q^{81} + 24 q^{82} - 160 q^{84} + 96 q^{85} + 80 q^{88} - 96 q^{90} - 320 q^{92} + 128 q^{93} - 40 q^{94} + 40 q^{96} + 320 q^{97} - 64 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)