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Properties

Label 2700.2.cn
Level $2700$
Weight $2$
Character orbit 2700.cn
Rep. character $\chi_{2700}(59,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $12864$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2700.cn (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2700 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).

Total New Old
Modular forms 13056 13056 0
Cusp forms 12864 12864 0
Eisenstein series 192 192 0

Trace form

\( 12864 q - 30 q^{2} - 18 q^{4} - 48 q^{5} - 18 q^{6} - 45 q^{8} - 36 q^{9} + O(q^{10}) \) \( 12864 q - 30 q^{2} - 18 q^{4} - 48 q^{5} - 18 q^{6} - 45 q^{8} - 36 q^{9} - 12 q^{10} - 30 q^{12} - 60 q^{13} - 18 q^{14} - 18 q^{16} - 90 q^{17} - 45 q^{20} - 36 q^{21} - 30 q^{22} - 30 q^{24} - 48 q^{25} - 60 q^{28} - 36 q^{29} - 33 q^{30} - 60 q^{33} - 30 q^{34} - 18 q^{36} - 30 q^{37} - 30 q^{38} - 39 q^{40} - 36 q^{41} + 120 q^{42} - 27 q^{44} - 48 q^{45} - 9 q^{46} - 30 q^{48} - 96 q^{49} + 54 q^{50} - 30 q^{52} - 18 q^{54} - 81 q^{56} - 30 q^{58} + 174 q^{60} - 36 q^{61} - 45 q^{62} - 9 q^{64} - 72 q^{65} - 153 q^{66} - 36 q^{69} + 66 q^{70} - 30 q^{72} - 30 q^{73} + 6 q^{74} - 24 q^{76} - 60 q^{77} + 75 q^{78} - 108 q^{81} + 132 q^{84} - 78 q^{85} + 42 q^{86} - 30 q^{88} - 54 q^{89} - 36 q^{90} - 30 q^{92} - 18 q^{94} - 18 q^{96} - 60 q^{97} - 45 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

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