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Properties

Label 832.4.p
Level $832$
Weight $4$
Character orbit 832.p
Rep. character $\chi_{832}(337,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $164$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 832.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
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 688 172 516
Cusp forms 656 164 492
Eisenstein series 32 8 24

Trace form

\( 164 q + 4 q^{3} + O(q^{10}) \) \( 164 q + 4 q^{3} - 2 q^{13} - 8 q^{17} + 160 q^{27} - 4 q^{29} + 504 q^{35} - 428 q^{43} + 6852 q^{49} + 112 q^{51} - 4 q^{53} - 4 q^{61} + 484 q^{65} + 104 q^{69} - 1708 q^{75} - 1376 q^{77} - 3152 q^{79} - 10700 q^{81} - 1960 q^{91} - 6072 q^{95} + O(q^{100}) \)

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

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