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Properties

Label 1800.4.bs
Level $1800$
Weight $4$
Character orbit 1800.bs
Rep. character $\chi_{1800}(289,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $448$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.bs (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).

Total New Old
Modular forms 4384 448 3936
Cusp forms 4256 448 3808
Eisenstein series 128 0 128

Trace form

\( 448 q + 4 q^{5} + O(q^{10}) \) \( 448 q + 4 q^{5} + 66 q^{11} + 114 q^{19} + 210 q^{23} + 126 q^{25} + 26 q^{29} - 414 q^{31} + 292 q^{35} - 20 q^{37} - 36 q^{41} + 860 q^{47} - 20556 q^{49} - 240 q^{53} + 292 q^{55} - 1554 q^{59} + 898 q^{61} - 376 q^{65} + 348 q^{71} + 2280 q^{73} + 168 q^{79} + 5190 q^{83} + 2052 q^{85} + 2370 q^{89} - 948 q^{91} - 2036 q^{95} + 2790 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)