Properties

Label 1900.3.cp
Level $1900$
Weight $3$
Character orbit 1900.cp
Rep. character $\chi_{1900}(29,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $2400$
Sturm bound $900$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.cp (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 14544 2400 12144
Cusp forms 14256 2400 11856
Eisenstein series 288 0 288

Trace form

\( 2400 q + O(q^{10}) \) \( 2400 q + 45 q^{11} + 123 q^{15} + 30 q^{23} + 270 q^{25} + 90 q^{29} + 270 q^{33} - 171 q^{35} - 630 q^{45} + 120 q^{47} + 8550 q^{49} + 300 q^{51} + 132 q^{55} - 360 q^{59} + 360 q^{61} - 1620 q^{65} + 330 q^{71} - 360 q^{79} + 240 q^{81} + 480 q^{83} + 630 q^{85} + 720 q^{87} - 180 q^{89} - 267 q^{95} + 270 q^{97} + 480 q^{99} + O(q^{100}) \)

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

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