↑

Properties

Label 3800.2.z
Level $3800$
Weight $2$
Character orbit 3800.z
Rep. character $\chi_{3800}(761,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $544$
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.z (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 2432 544 1888
Cusp forms 2368 544 1824
Eisenstein series 64 0 64

Trace form

\( 544 q + 2 q^{5} - 8 q^{7} - 140 q^{9} + O(q^{10}) \) \( 544 q + 2 q^{5} - 8 q^{7} - 140 q^{9} + 12 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{17} + 6 q^{19} - 18 q^{23} + 10 q^{25} - 4 q^{29} + 12 q^{31} + 24 q^{33} - 6 q^{35} - 42 q^{37} - 4 q^{41} + 22 q^{45} + 24 q^{47} + 600 q^{49} - 24 q^{51} + 42 q^{53} - 14 q^{55} + 8 q^{61} - 32 q^{63} - 26 q^{65} - 32 q^{67} + 24 q^{69} + 20 q^{73} - 36 q^{75} - 12 q^{77} - 32 q^{79} - 152 q^{81} - 58 q^{83} - 32 q^{85} - 8 q^{87} + 6 q^{89} - 32 q^{91} + 24 q^{93} - 88 q^{97} - 184 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)