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Properties

Label 3800.2.ek
Level $3800$
Weight $2$
Character orbit 3800.ek
Rep. character $\chi_{3800}(217,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2400$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.ek (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3800, [\chi])\).

Total New Old
Modular forms 9728 2400 7328
Cusp forms 9472 2400 7072
Eisenstein series 256 0 256

Trace form

\( 2400 q + O(q^{10}) \) \( 2400 q - 4 q^{23} + 8 q^{25} - 36 q^{33} + 80 q^{39} + 32 q^{43} - 128 q^{45} - 32 q^{47} - 40 q^{55} + 168 q^{57} - 120 q^{59} + 100 q^{63} + 72 q^{67} + 32 q^{73} - 8 q^{77} - 300 q^{81} + 80 q^{83} + 4 q^{85} - 344 q^{87} - 180 q^{93} + 68 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3800, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1900, [\chi])\)\(^{\oplus 2}\)