↑

Properties

Label 3850.2.fa
Level $3850$
Weight $2$
Character orbit 3850.fa
Rep. character $\chi_{3850}(479,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1920$
Sturm bound $1440$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3850.fa (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1925 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3850, [\chi])\).

Total New Old
Modular forms 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

\( 1920 q - 960 q^{4} + 12 q^{5} + 240 q^{9} + O(q^{10}) \) \( 1920 q - 960 q^{4} + 12 q^{5} + 240 q^{9} + 30 q^{10} + 4 q^{11} - 8 q^{15} - 960 q^{16} + 20 q^{22} + 10 q^{25} + 30 q^{28} + 6 q^{31} + 150 q^{33} + 60 q^{35} - 480 q^{36} + 10 q^{37} - 30 q^{40} + 50 q^{42} + 4 q^{44} + 138 q^{45} - 20 q^{46} - 12 q^{49} + 80 q^{50} + 40 q^{57} + 4 q^{60} + 30 q^{61} + 130 q^{63} + 1920 q^{64} + 48 q^{66} - 6 q^{70} - 16 q^{71} + 330 q^{75} + 10 q^{77} - 40 q^{79} - 12 q^{80} + 224 q^{81} - 200 q^{85} + 24 q^{86} - 10 q^{88} - 120 q^{89} + 4 q^{91} - 80 q^{93} - 40 q^{95} - 40 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)