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Properties

Label 2205.4.bf
Level $2205$
Weight $4$
Character orbit 2205.bf
Rep. character $\chi_{2205}(1549,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $592$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 2080 608 1472
Cusp forms 1952 592 1360
Eisenstein series 128 16 112

Trace form

\( 592 q + 1170 q^{4} - 5 q^{5} + O(q^{10}) \) \( 592 q + 1170 q^{4} - 5 q^{5} + 8 q^{10} - 52 q^{11} - 4586 q^{16} + 48 q^{19} - 368 q^{20} - 205 q^{25} + 218 q^{26} + 172 q^{29} + 6 q^{31} - 416 q^{34} + 106 q^{40} - 592 q^{41} - 1094 q^{44} - 514 q^{46} + 636 q^{50} - 1202 q^{55} - 322 q^{59} - 1568 q^{61} - 32484 q^{64} - 150 q^{65} - 4048 q^{71} + 6 q^{74} + 388 q^{76} - 3118 q^{79} - 3640 q^{80} - 4554 q^{85} - 5808 q^{86} - 2604 q^{89} + 3146 q^{94} + 3535 q^{95} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)