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Properties

Label 1200.4.cv
Level $1200$
Weight $4$
Character orbit 1200.cv
Rep. character $\chi_{1200}(127,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $720$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.cv (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1200, [\chi])\).

Total New Old
Modular forms 5856 720 5136
Cusp forms 5664 720 4944
Eisenstein series 192 0 192

Trace form

\( 720 q + O(q^{10}) \) \( 720 q - 276 q^{13} + 156 q^{17} - 132 q^{25} + 72 q^{33} - 396 q^{37} - 108 q^{45} + 1716 q^{53} + 1572 q^{65} - 3396 q^{73} - 3504 q^{77} + 14580 q^{81} + 2976 q^{85} + 660 q^{89} - 10944 q^{93} - 6204 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)