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Properties

Label 3900.2.ec
Level $3900$
Weight $2$
Character orbit 3900.ec
Rep. character $\chi_{3900}(161,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1120$
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.ec (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 975 \)
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 6816 1120 5696
Cusp forms 6624 1120 5504
Eisenstein series 192 0 192

Trace form

\( 1120 q + O(q^{10}) \) \( 1120 q - 24 q^{13} - 32 q^{15} - 12 q^{19} + 24 q^{27} - 54 q^{33} - 24 q^{37} - 24 q^{39} + 68 q^{45} + 16 q^{55} - 36 q^{57} + 32 q^{61} + 26 q^{63} - 48 q^{67} + 32 q^{73} - 32 q^{81} + 40 q^{85} - 32 q^{87} - 32 q^{91} + 4 q^{93} + 40 q^{97} - 40 q^{99} + O(q^{100}) \)

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

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