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Properties

Label 2205.4.cd
Level $2205$
Weight $4$
Character orbit 2205.cd
Rep. character $\chi_{2205}(932,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2912$
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.cd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 2992 1104
Cusp forms 3968 2912 1056
Eisenstein series 128 80 48

Trace form

\( 2912 q + 6 q^{2} + 8 q^{3} + 6 q^{5} + 24 q^{6} + O(q^{10}) \) \( 2912 q + 6 q^{2} + 8 q^{3} + 6 q^{5} + 24 q^{6} + 8 q^{10} + 36 q^{11} + 10 q^{12} + 2 q^{13} + 56 q^{15} + 22340 q^{16} - 376 q^{18} + 390 q^{20} + 22 q^{22} - 306 q^{23} - 142 q^{25} + 1004 q^{27} + 1170 q^{30} + 4 q^{31} + 1770 q^{32} - 818 q^{33} + 584 q^{36} + 152 q^{37} + 30 q^{38} - 126 q^{40} - 456 q^{41} - 10 q^{43} + 626 q^{45} + 1096 q^{46} + 3474 q^{47} + 2722 q^{48} - 702 q^{50} - 1952 q^{51} + 242 q^{52} + 1300 q^{55} + 2680 q^{57} - 534 q^{58} - 3182 q^{60} - 32 q^{61} + 2094 q^{65} + 5588 q^{66} + 614 q^{67} + 2694 q^{68} - 1342 q^{72} + 8 q^{73} + 1776 q^{75} + 864 q^{76} - 8650 q^{78} - 4612 q^{81} - 3704 q^{82} + 2826 q^{83} - 1666 q^{85} - 4128 q^{86} + 4738 q^{87} - 2934 q^{88} + 714 q^{90} + 5736 q^{92} - 2586 q^{93} + 7296 q^{95} - 10020 q^{96} + 362 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)