↑

Properties

Label 3800.2.v
Level $3800$
Weight $2$
Character orbit 3800.v
Rep. character $\chi_{3800}(2393,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $180$
Sturm bound $1200$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 1248 180 1068
Cusp forms 1152 180 972
Eisenstein series 96 0 96

Trace form

\( 180 q + O(q^{10}) \) \( 180 q + 16 q^{11} + 28 q^{23} - 16 q^{43} + 16 q^{47} - 32 q^{57} + 88 q^{63} - 32 q^{73} + 44 q^{77} - 244 q^{81} + 4 q^{83} + 8 q^{87} - 24 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 3}\)