↑

Properties

Label 1900.2.bq
Level $1900$
Weight $2$
Character orbit 1900.bq
Rep. character $\chi_{1900}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $400$
Sturm bound $600$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.bq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

Total New Old
Modular forms 2448 400 2048
Cusp forms 2352 400 1952
Eisenstein series 96 0 96

Trace form

\( 400 q - 2 q^{5} + 2 q^{7} + O(q^{10}) \) \( 400 q - 2 q^{5} + 2 q^{7} - 20 q^{17} + 20 q^{19} + 20 q^{23} - 14 q^{25} - 4 q^{35} + 80 q^{39} - 54 q^{43} - 120 q^{45} + 86 q^{47} - 64 q^{55} - 104 q^{57} + 78 q^{63} + 54 q^{73} - 170 q^{77} + 100 q^{81} - 28 q^{85} + 100 q^{87} + 72 q^{93} - 62 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

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