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Properties

Label 2205.2.do
Level $2205$
Weight $2$
Character orbit 2205.do
Rep. character $\chi_{2205}(89,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1344$
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.do (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
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 4128 1344 2784
Cusp forms 3936 1344 2592
Eisenstein series 192 0 192

Trace form

\( 1344 q + 112 q^{4} + O(q^{10}) \) \( 1344 q + 112 q^{4} + 12 q^{10} + 112 q^{16} + 24 q^{19} - 12 q^{25} + 24 q^{31} - 224 q^{34} + 184 q^{40} + 40 q^{46} + 104 q^{49} + 84 q^{55} - 88 q^{61} - 272 q^{64} - 64 q^{70} - 168 q^{76} + 32 q^{79} - 48 q^{85} - 144 q^{91} + 8 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)