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Properties

Label 2205.2.dg
Level $2205$
Weight $2$
Character orbit 2205.dg
Rep. character $\chi_{2205}(26,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $912$
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.dg (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
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 912 3216
Cusp forms 3936 912 3024
Eisenstein series 192 0 192

Trace form

\( 912 q - 80 q^{4} + 4 q^{7} + O(q^{10}) \) \( 912 q - 80 q^{4} + 4 q^{7} + 88 q^{16} - 12 q^{19} - 48 q^{22} + 76 q^{25} - 128 q^{28} - 12 q^{31} - 120 q^{37} - 24 q^{43} + 100 q^{49} + 336 q^{52} + 208 q^{58} - 84 q^{61} + 208 q^{64} - 12 q^{67} + 24 q^{70} + 84 q^{73} - 20 q^{79} + 144 q^{82} - 244 q^{91} - 304 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)