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Properties

Label 1900.3.cl
Level $1900$
Weight $3$
Character orbit 1900.cl
Rep. character $\chi_{1900}(21,\cdot)$
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.cl (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

\( 2400 q - 18 q^{7} + O(q^{10}) \) \( 2400 q - 18 q^{7} - 45 q^{11} - 141 q^{15} + 54 q^{17} - 126 q^{23} - 366 q^{25} + 90 q^{29} + 450 q^{33} + 9 q^{35} + 1284 q^{43} + 432 q^{45} + 72 q^{47} - 8250 q^{49} - 300 q^{51} - 18 q^{53} - 84 q^{55} + 1038 q^{57} - 360 q^{59} - 360 q^{61} - 144 q^{63} - 1620 q^{65} + 312 q^{67} - 330 q^{71} - 162 q^{73} - 252 q^{77} - 360 q^{79} - 240 q^{81} + 90 q^{83} - 6 q^{85} + 96 q^{87} - 180 q^{89} + 768 q^{93} + 39 q^{95} + 150 q^{97} + 480 q^{99} + O(q^{100}) \)

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

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