Properties

Label 1200.2.bq
Level $1200$
Weight $2$
Character orbit 1200.bq
Rep. character $\chi_{1200}(191,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $240$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.bq (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

Total New Old
Modular forms 1008 240 768
Cusp forms 912 240 672
Eisenstein series 96 0 96

Trace form

\( 240 q + O(q^{10}) \) \( 240 q - 12 q^{25} - 72 q^{37} - 12 q^{45} - 216 q^{49} + 48 q^{57} - 48 q^{61} + 24 q^{69} + 24 q^{73} + 72 q^{81} + 120 q^{85} + 24 q^{93} + 36 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

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