Properties

Label 2205.2.r
Level $2205$
Weight $2$
Character orbit 2205.r
Rep. character $\chi_{2205}(214,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $464$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 704 496 208
Cusp forms 640 464 176
Eisenstein series 64 32 32

Trace form

\( 464 q - 444 q^{4} - q^{5} + 10 q^{9} + O(q^{10}) \) \( 464 q - 444 q^{4} - q^{5} + 10 q^{9} - 2 q^{10} + 2 q^{11} - 24 q^{15} + 412 q^{16} + 4 q^{19} + 12 q^{20} - q^{25} + 32 q^{26} + 6 q^{29} - 29 q^{30} + 4 q^{31} + 8 q^{34} + 58 q^{39} + 8 q^{40} + 34 q^{41} - 40 q^{44} - 27 q^{45} + 14 q^{46} - 64 q^{50} + 30 q^{51} - 24 q^{54} + 30 q^{55} + 100 q^{59} + 29 q^{60} + 16 q^{61} - 376 q^{64} - 40 q^{65} - 40 q^{66} + 32 q^{69} - 76 q^{71} - 14 q^{74} - 42 q^{75} - 12 q^{76} + 4 q^{79} + 7 q^{80} + 2 q^{81} + q^{85} - 64 q^{86} - 40 q^{89} - 5 q^{90} - 4 q^{94} - 14 q^{95} - 48 q^{96} - 6 q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)