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Properties

Label 2205.2.ch
Level $2205$
Weight $2$
Character orbit 2205.ch
Rep. character $\chi_{2205}(313,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $928$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2205, [\chi])\).

Total New Old
Modular forms 1408 992 416
Cusp forms 1280 928 352
Eisenstein series 128 64 64

Trace form

\( 928 q - 2 q^{2} + 6 q^{3} - 40 q^{8} + O(q^{10}) \) \( 928 q - 2 q^{2} + 6 q^{3} - 40 q^{8} + 12 q^{10} - 8 q^{11} + 6 q^{12} - 22 q^{15} + 412 q^{16} + 30 q^{17} + 18 q^{18} + 48 q^{20} - 28 q^{23} + 4 q^{25} + 24 q^{26} - 36 q^{27} + 84 q^{30} + 12 q^{31} - 2 q^{32} - 24 q^{33} - 104 q^{36} + 4 q^{37} + 12 q^{41} - 8 q^{43} - 12 q^{45} + 20 q^{46} + 6 q^{47} + 18 q^{48} + 56 q^{50} + 52 q^{51} - 16 q^{53} - 8 q^{57} + 44 q^{58} + 14 q^{60} + 48 q^{61} - 50 q^{65} + 84 q^{66} - 2 q^{67} - 62 q^{72} + 12 q^{73} + 6 q^{75} + 48 q^{76} - 50 q^{78} - 12 q^{80} - 16 q^{81} + 24 q^{82} - 84 q^{83} - 8 q^{85} - 80 q^{86} + 24 q^{87} + 36 q^{88} + 36 q^{90} + 20 q^{92} - 96 q^{93} - 10 q^{95} - 72 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

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