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Properties

Label 2205.2.cz
Level $2205$
Weight $2$
Character orbit 2205.cz
Rep. character $\chi_{2205}(164,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $3984$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.cz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2205 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2205, [\chi])\).

Total New Old
Modular forms 4080 4080 0
Cusp forms 3984 3984 0
Eisenstein series 96 96 0

Trace form

\( 3984 q - 666 q^{4} - 18 q^{5} - 30 q^{6} - 16 q^{9} + O(q^{10}) \) \( 3984 q - 666 q^{4} - 18 q^{5} - 30 q^{6} - 16 q^{9} - 22 q^{10} - 36 q^{11} - 30 q^{14} - 16 q^{15} - 642 q^{16} - 72 q^{19} - 15 q^{20} - 16 q^{21} + 20 q^{24} - 8 q^{25} + 12 q^{26} - 48 q^{29} - 26 q^{30} - 2 q^{34} + 50 q^{36} - 30 q^{39} + 23 q^{40} - 48 q^{41} + 60 q^{44} + 147 q^{45} - 122 q^{46} - 6 q^{49} - 60 q^{50} + 10 q^{51} + 32 q^{54} - 70 q^{55} + 36 q^{56} - 30 q^{59} - 31 q^{60} - 14 q^{61} - 624 q^{64} - 21 q^{65} - 102 q^{66} - 88 q^{69} - 22 q^{70} + 126 q^{71} - 12 q^{74} - 176 q^{75} - 78 q^{76} + 69 q^{80} + 60 q^{81} - 106 q^{84} - 90 q^{86} + 138 q^{89} + 100 q^{90} - 76 q^{91} - 14 q^{94} - 21 q^{95} + 130 q^{96} + 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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