Properties

Label 2205.4.dk
Level $2205$
Weight $4$
Character orbit 2205.dk
Rep. character $\chi_{2205}(109,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $5016$
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.dk (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 12192 5064 7128
Cusp forms 12000 5016 6984
Eisenstein series 192 48 144

Trace form

\( 5016 q - 1690 q^{4} + 9 q^{5} + O(q^{10}) \) \( 5016 q - 1690 q^{4} + 9 q^{5} - 6 q^{10} - 212 q^{11} + 138 q^{14} + 6522 q^{16} - 1030 q^{19} + 94 q^{20} - 83 q^{25} + 778 q^{26} + 118 q^{29} + 2596 q^{31} - 752 q^{34} - 389 q^{35} - 1420 q^{40} - 788 q^{41} - 3902 q^{44} + 3058 q^{46} + 2674 q^{49} - 4682 q^{50} + 674 q^{55} + 2092 q^{56} - 476 q^{59} + 4452 q^{61} + 52168 q^{64} - 380 q^{65} - 4646 q^{70} + 3968 q^{71} - 3898 q^{74} + 3398 q^{76} - 684 q^{79} + 756 q^{80} - 460 q^{85} + 420 q^{86} - 12096 q^{89} - 2930 q^{91} + 4210 q^{94} - 8144 q^{95} + O(q^{100}) \)

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

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