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Properties

Label 1800.4.cc
Level $1800$
Weight $4$
Character orbit 1800.cc
Rep. character $\chi_{1800}(181,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1792$
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.cc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
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 4352 1808 2544
Cusp forms 4288 1792 2496
Eisenstein series 64 16 48

Trace form

\( 1792 q + 3 q^{2} - 3 q^{4} - 16 q^{7} + 66 q^{8} + O(q^{10}) \) \( 1792 q + 3 q^{2} - 3 q^{4} - 16 q^{7} + 66 q^{8} - 51 q^{10} - 39 q^{14} - 111 q^{16} + 58 q^{17} + 153 q^{20} - 430 q^{22} + 6 q^{23} + 14 q^{25} + 14 q^{26} - 945 q^{28} - 378 q^{31} - 282 q^{32} + 157 q^{34} + 1151 q^{38} - 90 q^{40} + 242 q^{41} + 530 q^{44} - 407 q^{46} - 402 q^{47} + 85440 q^{49} - 241 q^{50} + 184 q^{52} - 402 q^{55} + 1590 q^{56} + 1508 q^{58} - 232 q^{62} - 2388 q^{64} + 2436 q^{65} + 2434 q^{68} + 608 q^{70} - 1982 q^{71} + 734 q^{73} + 1060 q^{74} - 1932 q^{76} - 1586 q^{79} + 4014 q^{80} - 9618 q^{82} - 4631 q^{86} - 3376 q^{88} + 336 q^{89} - 2310 q^{92} + 1121 q^{94} - 290 q^{95} - 3146 q^{97} - 1580 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)