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Properties

Label 2205.2.u
Level $2205$
Weight $2$
Character orbit 2205.u
Rep. character $\chi_{2205}(374,\cdot)$
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.u (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

\( 464 q - 226 q^{4} + 6 q^{5} - 12 q^{6} + 8 q^{9} + O(q^{10}) \) \( 464 q - 226 q^{4} + 6 q^{5} - 12 q^{6} + 8 q^{9} + 6 q^{10} + 2 q^{15} - 214 q^{16} + 12 q^{19} - 6 q^{20} + 42 q^{24} + 2 q^{25} - 12 q^{26} - 42 q^{29} + 64 q^{30} + 6 q^{31} - 12 q^{34} + 40 q^{36} + 20 q^{39} + 6 q^{41} + 36 q^{44} + 12 q^{45} - 6 q^{46} - 60 q^{50} - 26 q^{51} + 48 q^{54} + 6 q^{59} + 16 q^{60} - 12 q^{61} + 344 q^{64} - 90 q^{65} - 78 q^{66} + 60 q^{69} - 12 q^{75} - 48 q^{76} - 2 q^{79} - 69 q^{80} - 68 q^{81} + q^{85} + 72 q^{89} + 33 q^{90} + 6 q^{94} + 27 q^{95} + 12 q^{96} - 58 q^{99} + O(q^{100}) \)

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.

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

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