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Properties

Label 2205.4.u
Level $2205$
Weight $4$
Character orbit 2205.u
Rep. character $\chi_{2205}(374,\cdot)$
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.u (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

\( 1424 q - 2818 q^{4} + 6 q^{5} - 48 q^{6} - 16 q^{9} + O(q^{10}) \) \( 1424 q - 2818 q^{4} + 6 q^{5} - 48 q^{6} - 16 q^{9} + 6 q^{10} - 169 q^{15} - 11026 q^{16} + 12 q^{19} - 24 q^{20} + 24 q^{24} + 2 q^{25} - 48 q^{26} - 150 q^{29} - 314 q^{30} + 6 q^{31} - 48 q^{34} - 1160 q^{36} + 1298 q^{39} + 618 q^{41} + 1872 q^{44} + 687 q^{45} - 312 q^{46} - 1932 q^{50} - 1538 q^{51} - 2220 q^{54} + 6 q^{59} + 3610 q^{60} - 48 q^{61} + 84224 q^{64} + 3267 q^{65} - 2922 q^{66} - 1686 q^{69} - 1407 q^{75} - 480 q^{76} - 1190 q^{79} + 3855 q^{80} - 1028 q^{81} + 121 q^{85} + 1854 q^{89} - 507 q^{90} + 6 q^{94} - 3861 q^{95} + 4422 q^{96} + 7070 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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