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Properties

Label 1800.4.z
Level $1800$
Weight $4$
Character orbit 1800.z
Rep. character $\chi_{1800}(361,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $452$
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.z (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 4384 452 3932
Cusp forms 4256 452 3804
Eisenstein series 128 0 128

Trace form

\( 452 q + 7 q^{5} + 12 q^{7} + O(q^{10}) \) \( 452 q + 7 q^{5} + 12 q^{7} - 66 q^{11} - 66 q^{13} + 86 q^{17} + 114 q^{19} - 230 q^{23} - 87 q^{25} - 104 q^{29} + 414 q^{31} - 304 q^{35} - 525 q^{37} + 266 q^{41} + 224 q^{43} + 1680 q^{47} + 23544 q^{49} + 939 q^{53} - 1184 q^{55} - 1554 q^{59} - 68 q^{61} - 2065 q^{65} + 936 q^{67} - 348 q^{71} + 402 q^{73} - 352 q^{77} + 168 q^{79} + 4958 q^{83} - 2397 q^{85} - 135 q^{89} + 948 q^{91} - 3560 q^{95} + 1128 q^{97} + O(q^{100}) \)

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

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