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Properties

Label 1200.3.ch
Level $1200$
Weight $3$
Character orbit 1200.ch
Rep. character $\chi_{1200}(19,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1920$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.ch (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1200, [\chi])\).

Total New Old
Modular forms 3872 1920 1952
Cusp forms 3808 1920 1888
Eisenstein series 64 0 64

Trace form

\( 1920 q + 60 q^{8} + O(q^{10}) \) \( 1920 q + 60 q^{8} - 36 q^{10} - 200 q^{26} - 72 q^{30} - 160 q^{34} - 96 q^{35} + 628 q^{40} - 420 q^{44} - 13440 q^{49} + 64 q^{50} + 540 q^{52} - 256 q^{55} - 72 q^{60} - 540 q^{64} + 128 q^{65} - 1440 q^{67} + 480 q^{70} + 440 q^{74} + 192 q^{75} - 120 q^{76} + 472 q^{80} + 4320 q^{81} - 1980 q^{88} - 24 q^{90} - 2340 q^{92} - 860 q^{94} + 900 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)