↑

Properties

Label 1900.2.bm
Level $1900$
Weight $2$
Character orbit 1900.bm
Rep. character $\chi_{1900}(149,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $180$
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.bm (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 1908 180 1728
Cusp forms 1692 180 1512
Eisenstein series 216 0 216

Trace form

\( 180 q + O(q^{10}) \) \( 180 q + 6 q^{11} + 12 q^{19} - 12 q^{21} - 12 q^{29} + 48 q^{39} + 12 q^{41} + 60 q^{49} - 102 q^{51} + 66 q^{59} - 42 q^{61} + 48 q^{69} - 36 q^{71} - 24 q^{79} + 144 q^{81} + 60 q^{89} + 126 q^{91} + 48 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)