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Properties

Label 832.4.u
Level $832$
Weight $4$
Character orbit 832.u
Rep. character $\chi_{832}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $168$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 832.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(832, [\chi])\).

Total New Old
Modular forms 696 168 528
Cusp forms 648 168 480
Eisenstein series 48 0 48

Trace form

\( 168 q + 1512 q^{9} + O(q^{10}) \) \( 168 q + 1512 q^{9} - 1416 q^{41} + 672 q^{57} + 3144 q^{65} + 1752 q^{73} + 13608 q^{81} + 264 q^{89} - 2280 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(832, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)