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Properties

Label 1900.3.y
Level $1900$
Weight $3$
Character orbit 1900.y
Rep. character $\chi_{1900}(39,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2160$
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.y (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 2416 2160 256
Cusp forms 2384 2160 224
Eisenstein series 32 0 32

Trace form

\( 2160 q - 4 q^{5} - 1620 q^{9} + O(q^{10}) \) \( 2160 q - 4 q^{5} - 1620 q^{9} + 8 q^{10} - 120 q^{16} + 76 q^{25} + 40 q^{29} - 100 q^{30} + 160 q^{34} - 300 q^{36} + 100 q^{37} - 44 q^{40} + 200 q^{41} + 700 q^{42} - 108 q^{45} - 200 q^{46} + 130 q^{48} + 14960 q^{49} + 186 q^{50} + 430 q^{52} - 140 q^{53} - 390 q^{54} + 180 q^{56} - 1272 q^{60} - 200 q^{61} - 68 q^{65} + 690 q^{66} + 480 q^{69} - 200 q^{70} + 220 q^{74} - 1430 q^{78} + 230 q^{80} - 4860 q^{81} - 1100 q^{84} + 452 q^{85} + 600 q^{86} - 990 q^{88} + 780 q^{89} - 268 q^{90} - 1170 q^{92} - 480 q^{94} + 1280 q^{96} + 400 q^{97} - 140 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)