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Properties

Label 2205.4.cp
Level $2205$
Weight $4$
Character orbit 2205.cp
Rep. character $\chi_{2205}(251,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1344$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.cp (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2205, [\chi])\).

Total New Old
Modular forms 6096 1344 4752
Cusp forms 6000 1344 4656
Eisenstein series 96 0 96

Trace form

\( 1344 q + 896 q^{4} - 64 q^{7} + O(q^{10}) \) \( 1344 q + 896 q^{4} - 64 q^{7} - 3584 q^{16} - 1008 q^{22} - 5600 q^{25} + 304 q^{28} + 2408 q^{37} - 224 q^{43} - 3128 q^{49} - 224 q^{52} + 3360 q^{58} + 13048 q^{61} + 6272 q^{64} + 2912 q^{67} + 1080 q^{70} + 896 q^{79} + 2016 q^{88} - 16128 q^{91} - 10752 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

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