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Properties

Label 2205.2.db
Level $2205$
Weight $2$
Character orbit 2205.db
Rep. character $\chi_{2205}(4,\cdot)$
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.db (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

\( 3984 q - 344 q^{4} - 5 q^{5} - 14 q^{6} + O(q^{10}) \) \( 3984 q - 344 q^{4} - 5 q^{5} - 14 q^{6} - 30 q^{10} - 10 q^{11} - 6 q^{14} - 10 q^{15} + 308 q^{16} - 24 q^{19} + 5 q^{20} - 20 q^{21} - 46 q^{24} - 5 q^{25} - 24 q^{26} + 38 q^{29} + 15 q^{30} + 12 q^{31} - 6 q^{34} - 52 q^{35} + 70 q^{36} - 4 q^{39} - 23 q^{40} + 20 q^{41} - 32 q^{44} + 25 q^{45} + 18 q^{46} - 24 q^{50} - 26 q^{51} - 28 q^{54} - 40 q^{55} - 32 q^{56} - 64 q^{59} - 60 q^{60} - 22 q^{61} + 576 q^{64} - 11 q^{65} - 150 q^{66} + 4 q^{69} + 17 q^{70} - 10 q^{71} + 62 q^{74} - 62 q^{75} - 82 q^{76} + 24 q^{79} - 7 q^{80} - 176 q^{81} - 312 q^{84} + 34 q^{86} - 166 q^{89} - 145 q^{90} - 20 q^{91} - 12 q^{94} - 5 q^{95} - 14 q^{96} - 126 q^{99} + O(q^{100}) \)

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.