Properties

Label 2205.2.cf
Level $2205$
Weight $2$
Character orbit 2205.cf
Rep. character $\chi_{2205}(422,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
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.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
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 1472 320 1152
Cusp forms 1216 320 896
Eisenstein series 256 0 256

Trace form

\( 320 q + O(q^{10}) \) \( 320 q - 8 q^{10} + 160 q^{16} + 80 q^{22} + 32 q^{25} - 32 q^{31} + 32 q^{37} + 40 q^{40} + 16 q^{43} + 80 q^{52} + 32 q^{55} + 136 q^{58} - 48 q^{61} + 32 q^{67} + 88 q^{73} + 320 q^{76} + 56 q^{82} + 16 q^{85} - 216 q^{88} - 208 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)