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Properties

Label 2205.4.bt
Level $2205$
Weight $4$
Character orbit 2205.bt
Rep. character $\chi_{2205}(178,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2848$
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.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4096 2912 1184
Cusp forms 3968 2848 1120
Eisenstein series 128 64 64

Trace form

\( 2848 q + 4 q^{2} + 6 q^{3} + 6 q^{5} - 64 q^{8} + O(q^{10}) \) \( 2848 q + 4 q^{2} + 6 q^{3} + 6 q^{5} - 64 q^{8} + 12 q^{10} - 20 q^{11} + 54 q^{12} + 68 q^{15} - 44024 q^{16} - 132 q^{17} + 162 q^{18} - 768 q^{20} + 24 q^{22} + 206 q^{23} - 2 q^{25} + 24 q^{26} - 828 q^{27} + 1494 q^{30} - 2348 q^{32} + 6 q^{33} + 64 q^{36} + 4 q^{37} + 6 q^{38} + 6 q^{40} - 1236 q^{41} - 8 q^{43} - 1386 q^{45} - 496 q^{46} - 270 q^{48} + 2696 q^{50} - 1772 q^{51} - 762 q^{52} - 556 q^{53} - 4124 q^{57} + 470 q^{58} + 1226 q^{60} - 2780 q^{65} + 12 q^{66} + 4 q^{67} + 2214 q^{68} + 4608 q^{71} - 7358 q^{72} + 12 q^{73} - 3546 q^{75} - 768 q^{76} - 10274 q^{78} - 372 q^{80} - 2644 q^{81} + 60 q^{82} - 168 q^{83} - 8 q^{85} - 872 q^{86} - 3630 q^{87} - 1218 q^{88} - 5976 q^{90} + 2216 q^{92} - 1446 q^{93} + 2900 q^{95} + 8736 q^{96} + O(q^{100}) \)

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

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