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Properties

Label 1200.3.q
Level $1200$
Weight $3$
Character orbit 1200.q
Rep. character $\chi_{1200}(499,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
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.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 984 288 696
Cusp forms 936 288 648
Eisenstein series 48 0 48

Trace form

\( 288 q + O(q^{10}) \) \( 288 q - 32 q^{14} - 56 q^{16} - 64 q^{19} + 72 q^{24} - 200 q^{26} - 248 q^{34} - 24 q^{36} + 632 q^{44} + 56 q^{46} - 2016 q^{49} + 192 q^{51} - 72 q^{54} - 168 q^{56} - 256 q^{59} + 64 q^{61} + 624 q^{64} - 144 q^{66} + 192 q^{69} - 1024 q^{71} + 176 q^{74} - 32 q^{76} - 2592 q^{81} - 992 q^{86} + 768 q^{91} - 232 q^{94} - 600 q^{96} + O(q^{100}) \)

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

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