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Properties

Label 2205.2.bw
Level $2205$
Weight $2$
Character orbit 2205.bw
Rep. character $\chi_{2205}(263,\cdot)$
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.bw (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

\( 928 q + 2 q^{3} + 6 q^{5} + 24 q^{6} + O(q^{10}) \) \( 928 q + 2 q^{3} + 6 q^{5} + 24 q^{6} + 4 q^{10} + 36 q^{11} - 26 q^{12} + 4 q^{13} - 10 q^{15} - 824 q^{16} - 18 q^{17} - 46 q^{18} + 12 q^{20} - 16 q^{22} + 54 q^{23} - 2 q^{25} + 32 q^{27} - 30 q^{30} + 8 q^{31} + 34 q^{33} - 40 q^{36} + 4 q^{37} + 30 q^{38} - 18 q^{40} + 36 q^{41} - 8 q^{43} - 22 q^{45} - 4 q^{46} - 38 q^{48} - 72 q^{50} + 76 q^{51} - 26 q^{52} - 4 q^{55} - 80 q^{57} - 6 q^{58} - 50 q^{60} - 16 q^{61} - 4 q^{66} + 4 q^{67} - 114 q^{68} + 206 q^{72} + 4 q^{73} - 6 q^{75} + 24 q^{76} - 22 q^{78} + 36 q^{80} + 68 q^{81} + 8 q^{82} + 12 q^{83} - 8 q^{85} + 120 q^{86} + 28 q^{87} - 18 q^{88} + 24 q^{90} - 180 q^{92} - 18 q^{93} - 192 q^{96} + 4 q^{97} + O(q^{100}) \)

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

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