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Properties

Label 2205.4.bs
Level $2205$
Weight $4$
Character orbit 2205.bs
Rep. character $\chi_{2205}(316,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $1680$
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.bs (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 6096 1680 4416
Cusp forms 6000 1680 4320
Eisenstein series 96 0 96

Trace form

\( 1680 q - 1120 q^{4} - 10 q^{5} + 44 q^{7} + O(q^{10}) \) \( 1680 q - 1120 q^{4} - 10 q^{5} + 44 q^{7} + 20 q^{10} + 28 q^{11} - 52 q^{13} + 432 q^{14} - 4424 q^{16} - 128 q^{17} + 68 q^{19} - 160 q^{20} - 616 q^{22} + 420 q^{23} - 7000 q^{25} + 856 q^{26} + 966 q^{28} - 378 q^{29} + 392 q^{31} + 1120 q^{32} + 820 q^{34} + 800 q^{35} - 1036 q^{37} - 596 q^{38} + 240 q^{40} + 1416 q^{41} - 224 q^{43} - 840 q^{44} - 2352 q^{46} - 1200 q^{47} + 492 q^{49} + 4280 q^{52} + 2072 q^{53} + 200 q^{55} - 2678 q^{56} - 308 q^{58} + 1758 q^{59} - 6592 q^{61} + 3560 q^{62} - 18032 q^{64} - 420 q^{65} + 2016 q^{67} + 11540 q^{68} - 1340 q^{70} - 952 q^{71} + 96 q^{73} + 4816 q^{74} - 868 q^{76} - 2152 q^{77} + 1120 q^{79} + 6400 q^{80} + 6478 q^{82} + 380 q^{83} - 560 q^{85} + 1316 q^{86} - 2590 q^{88} - 4904 q^{89} + 5286 q^{91} - 11774 q^{92} - 766 q^{94} + 560 q^{95} - 968 q^{97} - 10926 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)