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Properties

Label 2205.2.dk
Level $2205$
Weight $2$
Character orbit 2205.dk
Rep. character $\chi_{2205}(109,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1656$
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.dk (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 4128 1704 2424
Cusp forms 3936 1656 2280
Eisenstein series 192 48 144

Trace form

\( 1656 q - 162 q^{4} + 14 q^{5} + O(q^{10}) \) \( 1656 q - 162 q^{4} + 14 q^{5} - 14 q^{10} + 12 q^{11} + 12 q^{14} + 106 q^{16} + 38 q^{19} - 18 q^{20} - 6 q^{25} + 26 q^{26} + 54 q^{29} - 70 q^{31} - 96 q^{34} - 12 q^{35} - 70 q^{40} + 36 q^{41} + 100 q^{44} - 74 q^{46} - 70 q^{49} + 158 q^{50} - 15 q^{55} + 34 q^{56} + 66 q^{59} + 50 q^{61} + 144 q^{64} + 34 q^{65} - 48 q^{70} + 86 q^{71} + 38 q^{74} - 70 q^{76} + 16 q^{79} + 82 q^{80} + 34 q^{85} - 82 q^{86} - 8 q^{89} - 130 q^{91} - 42 q^{94} + 103 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)