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Properties

Label 2205.4.d
Level $2205$
Weight $4$
Character orbit 2205.d
Rep. character $\chi_{2205}(1324,\cdot)$
Character field $\Q$
Dimension $302$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1040 312 728
Cusp forms 976 302 674
Eisenstein series 64 10 54

Trace form

\( 302 q - 1176 q^{4} - 16 q^{5} + O(q^{10}) \) \( 302 q - 1176 q^{4} - 16 q^{5} - 68 q^{10} + 4 q^{11} + 4448 q^{16} - 144 q^{19} + 236 q^{20} + 4 q^{25} + 64 q^{26} - 256 q^{29} + 336 q^{31} - 484 q^{34} + 896 q^{40} - 476 q^{41} + 944 q^{44} - 284 q^{46} - 1188 q^{50} - 1312 q^{55} + 1588 q^{59} - 688 q^{61} - 14712 q^{64} - 1980 q^{65} + 1240 q^{71} - 912 q^{74} + 4664 q^{76} - 260 q^{79} - 2204 q^{80} - 774 q^{85} + 6216 q^{86} - 420 q^{89} - 1196 q^{94} + 1658 q^{95} + O(q^{100}) \)

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

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