Properties

Label 1200.4.bq
Level $1200$
Weight $4$
Character orbit 1200.bq
Rep. character $\chi_{1200}(191,\cdot)$
Character field $\Q(\zeta_{10})$
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.bq (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 2928 720 2208
Cusp forms 2832 720 2112
Eisenstein series 96 0 96

Trace form

\( 720 q + O(q^{10}) \) \( 720 q + 252 q^{25} + 2376 q^{37} + 492 q^{45} - 34056 q^{49} - 2544 q^{57} - 1872 q^{61} + 744 q^{69} + 2952 q^{73} + 1368 q^{81} + 8712 q^{85} + 2472 q^{93} - 3348 q^{97} + O(q^{100}) \)

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

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