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Properties

Label 2205.2.cd
Level $2205$
Weight $2$
Character orbit 2205.cd
Rep. character $\chi_{2205}(932,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $944$
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.cd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 1024 384
Cusp forms 1280 944 336
Eisenstein series 128 80 48

Trace form

\( 944 q + 6 q^{2} + 2 q^{3} + 6 q^{5} + O(q^{10}) \) \( 944 q + 6 q^{2} + 2 q^{3} + 6 q^{5} + 8 q^{10} + 22 q^{12} + 2 q^{13} - 34 q^{15} + 416 q^{16} + 44 q^{18} + 30 q^{20} - 2 q^{22} - 18 q^{23} + 8 q^{25} + 14 q^{27} - 30 q^{30} + 4 q^{31} - 30 q^{32} + 28 q^{33} + 32 q^{36} + 20 q^{37} - 42 q^{38} - 6 q^{40} - 24 q^{41} - 10 q^{43} - 4 q^{45} + 16 q^{46} - 74 q^{48} + 18 q^{50} + 28 q^{51} + 14 q^{52} + 40 q^{55} - 38 q^{57} + 6 q^{58} + 58 q^{60} - 8 q^{61} - 66 q^{65} + 44 q^{66} + 8 q^{67} - 42 q^{68} - 70 q^{72} + 8 q^{73} + 66 q^{75} + 2 q^{78} + 8 q^{81} + 64 q^{82} - 54 q^{83} + 14 q^{85} + 192 q^{86} - 98 q^{87} + 6 q^{88} - 186 q^{90} - 204 q^{92} + 114 q^{93} + 96 q^{95} + 120 q^{96} + 32 q^{97} + O(q^{100}) \)

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

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