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Properties

Label 1800.2.cc
Level $1800$
Weight $2$
Character orbit 1800.cc
Rep. character $\chi_{1800}(181,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $592$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.cc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).

Total New Old
Modular forms 1472 608 864
Cusp forms 1408 592 816
Eisenstein series 64 16 48

Trace form

\( 592 q + 3 q^{2} - 3 q^{4} - 16 q^{7} - 6 q^{8} + O(q^{10}) \) \( 592 q + 3 q^{2} - 3 q^{4} - 16 q^{7} - 6 q^{8} + q^{10} + 3 q^{14} - 15 q^{16} + 2 q^{17} - 7 q^{20} + 6 q^{23} - 6 q^{25} + 22 q^{26} - 5 q^{28} + 6 q^{31} + 38 q^{32} - 15 q^{34} + 51 q^{38} - 50 q^{40} + 10 q^{41} - 10 q^{44} + 21 q^{46} - 18 q^{47} + 528 q^{49} + 71 q^{50} - 76 q^{52} - 34 q^{55} + 6 q^{56} - 38 q^{58} + 62 q^{62} + 12 q^{64} - 24 q^{65} + 18 q^{68} - 32 q^{70} + 34 q^{71} - 26 q^{73} + 48 q^{74} - 20 q^{76} + 14 q^{79} - 74 q^{80} - 42 q^{82} + 7 q^{86} - 72 q^{88} + 36 q^{89} - 50 q^{92} + 29 q^{94} + 110 q^{95} + 14 q^{97} + 138 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

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