↑

Properties

Label 1900.3.p
Level $1900$
Weight $3$
Character orbit 1900.p
Rep. character $\chi_{1900}(449,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $900$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1900, [\chi])\).

Total New Old
Modular forms 1236 120 1116
Cusp forms 1164 120 1044
Eisenstein series 72 0 72

Trace form

\( 120 q - 180 q^{9} + O(q^{10}) \) \( 120 q - 180 q^{9} + 36 q^{11} - 40 q^{19} - 18 q^{21} + 60 q^{29} - 164 q^{39} - 24 q^{41} - 1032 q^{49} + 282 q^{51} - 132 q^{59} - 36 q^{61} - 390 q^{71} - 372 q^{79} - 1012 q^{81} + 78 q^{89} + 126 q^{91} - 122 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

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