Properties

Label 2205.4.bq
Level $2205$
Weight $4$
Character orbit 2205.bq
Rep. character $\chi_{2205}(509,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1424$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2205, [\chi])\).

Total New Old
Modular forms 2048 1456 592
Cusp forms 1984 1424 560
Eisenstein series 64 32 32

Trace form

\( 1424 q + 5636 q^{4} + 3 q^{5} + 48 q^{6} - 58 q^{9} + O(q^{10}) \) \( 1424 q + 5636 q^{4} + 3 q^{5} + 48 q^{6} - 58 q^{9} + 6 q^{10} - 18 q^{11} - 169 q^{15} + 22052 q^{16} + 12 q^{19} + 24 q^{20} + 552 q^{24} - q^{25} + 48 q^{26} - 150 q^{29} + 259 q^{30} + 48 q^{34} - 1160 q^{36} - 2452 q^{39} + 426 q^{40} - 618 q^{41} - 1872 q^{44} + 699 q^{45} - 312 q^{46} - 1932 q^{50} + 1018 q^{51} - 2172 q^{54} + 12 q^{59} - 881 q^{60} + 84224 q^{64} + 168 q^{66} + 1686 q^{69} - 186 q^{74} - 3579 q^{75} + 480 q^{76} + 2380 q^{79} - 3855 q^{80} - 482 q^{81} + 121 q^{85} + 20844 q^{86} - 1854 q^{89} + 507 q^{90} + 1356 q^{96} + 7070 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)