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Properties

Label 2205.4.by
Level $2205$
Weight $4$
Character orbit 2205.by
Rep. character $\chi_{2205}(128,\cdot)$
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.by (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

\( 2848 q + 6 q^{2} + 2 q^{3} + O(q^{10}) \) \( 2848 q + 6 q^{2} + 2 q^{3} + 4 q^{10} + 142 q^{12} + 4 q^{13} - 100 q^{15} + 22012 q^{16} - 144 q^{17} + 2 q^{18} + 12 q^{20} - 40 q^{22} + 4 q^{25} - 4 q^{27} - 2400 q^{30} - 4 q^{31} - 2370 q^{32} + 106 q^{33} - 1984 q^{36} + 4 q^{37} + 516 q^{40} + 1260 q^{41} - 8 q^{43} - 382 q^{45} + 512 q^{46} + 6 q^{47} - 1778 q^{48} + 648 q^{50} - 2300 q^{51} + 580 q^{52} - 484 q^{55} + 1180 q^{57} - 1068 q^{58} + 1018 q^{60} + 32 q^{61} - 4170 q^{65} - 2764 q^{66} - 2 q^{67} - 3718 q^{72} + 4 q^{73} - 534 q^{75} + 264 q^{76} - 934 q^{78} - 1116 q^{80} + 3824 q^{81} + 20 q^{82} + 12 q^{83} - 8 q^{85} - 3584 q^{87} - 1404 q^{88} + 1524 q^{90} - 7560 q^{92} + 4650 q^{93} - 2994 q^{95} + 5364 q^{96} + 4 q^{97} + O(q^{100}) \)

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

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