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Properties

Label 539.4.b
Level $539$
Weight $4$
Character orbit 539.b
Rep. character $\chi_{539}(538,\cdot)$
Character field $\Q$
Dimension $116$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 539.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(539, [\chi])\).

Total New Old
Modular forms 176 124 52
Cusp forms 160 116 44
Eisenstein series 16 8 8

Trace form

\( 116 q - 424 q^{4} - 904 q^{9} + O(q^{10}) \) \( 116 q - 424 q^{4} - 904 q^{9} + 30 q^{11} - 364 q^{15} + 1232 q^{16} + 576 q^{22} - 604 q^{23} - 1912 q^{25} + 940 q^{36} + 588 q^{37} - 1792 q^{44} - 3828 q^{53} + 1468 q^{58} + 6112 q^{60} - 8188 q^{64} + 4036 q^{67} - 4728 q^{71} + 1768 q^{78} + 3084 q^{81} + 636 q^{86} - 8056 q^{88} + 4748 q^{92} + 2908 q^{93} + 2776 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(539, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(539, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(539, [\chi]) \cong \)