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Properties

Label 832.4.n
Level $832$
Weight $4$
Character orbit 832.n
Rep. character $\chi_{832}(209,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 832.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 688 144 544
Cusp forms 656 144 512
Eisenstein series 32 0 32

Trace form

\( 144 q + O(q^{10}) \) \( 144 q + 40 q^{11} - 240 q^{15} - 48 q^{19} + 400 q^{29} + 744 q^{31} + 456 q^{35} + 16 q^{37} - 1240 q^{43} - 1880 q^{47} - 7056 q^{49} - 2888 q^{51} + 752 q^{53} - 1824 q^{61} + 2520 q^{63} + 3888 q^{67} - 1056 q^{69} - 4408 q^{75} + 1904 q^{77} - 5664 q^{79} - 11664 q^{81} - 2440 q^{83} - 480 q^{85} + 7728 q^{95} + 1800 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)