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Properties

Label 1800.4.q
Level $1800$
Weight $4$
Character orbit 1800.q
Rep. character $\chi_{1800}(601,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $342$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2208 342 1866
Cusp forms 2112 342 1770
Eisenstein series 96 0 96

Trace form

\( 342 q + q^{3} + q^{9} + O(q^{10}) \) \( 342 q + q^{3} + q^{9} - 91 q^{11} + 22 q^{17} - 90 q^{19} - 148 q^{21} + 52 q^{23} - 452 q^{27} + 132 q^{29} + 90 q^{31} - 149 q^{33} + 98 q^{39} + 519 q^{41} - 297 q^{43} - 516 q^{47} - 8577 q^{49} + 1229 q^{51} + 1160 q^{53} + 505 q^{57} - 763 q^{59} + 18 q^{61} - 2294 q^{63} - 387 q^{67} + 530 q^{69} + 1192 q^{71} + 1242 q^{73} - 572 q^{77} - 126 q^{79} - 1355 q^{81} + 1506 q^{83} + 376 q^{87} + 708 q^{89} + 1980 q^{91} - 4378 q^{93} + 423 q^{97} + 1050 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)