↑

Properties

Label 2050.2.dg
Level $2050$
Weight $2$
Character orbit 2050.dg
Rep. character $\chi_{2050}(17,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1680$
Sturm bound $630$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2050 = 2 \cdot 5^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2050.dg (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1025 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(630\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2050, [\chi])\).

Total New Old
Modular forms 5104 1680 3424
Cusp forms 4976 1680 3296
Eisenstein series 128 0 128

Trace form

\( 1680 q + 420 q^{4} + O(q^{10}) \) \( 1680 q + 420 q^{4} + 32 q^{13} + 8 q^{15} - 420 q^{16} - 20 q^{17} + 16 q^{22} - 24 q^{27} - 20 q^{29} - 16 q^{30} - 120 q^{33} - 40 q^{35} + 48 q^{37} + 120 q^{41} + 32 q^{42} - 80 q^{45} + 8 q^{47} + 36 q^{50} - 52 q^{52} - 4 q^{53} - 16 q^{55} - 120 q^{57} - 8 q^{58} - 88 q^{60} - 20 q^{61} - 32 q^{62} - 208 q^{63} + 420 q^{64} + 24 q^{65} + 48 q^{67} + 20 q^{68} - 80 q^{69} + 120 q^{71} + 136 q^{75} - 120 q^{77} - 68 q^{82} + 80 q^{83} - 96 q^{85} + 192 q^{87} - 16 q^{88} + 64 q^{90} - 168 q^{93} + 48 q^{95} - 104 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2050, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2050, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1025, [\chi])\)\(^{\oplus 2}\)