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Properties

Label 832.4.bn
Level $832$
Weight $4$
Character orbit 832.bn
Rep. character $\chi_{832}(175,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $328$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 832.bn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1376 344 1032
Cusp forms 1312 328 984
Eisenstein series 64 16 48

Trace form

\( 328 q + 2 q^{3} + 8 q^{7} + O(q^{10}) \) \( 328 q + 2 q^{3} + 8 q^{7} + 6 q^{11} - 4 q^{13} - 216 q^{15} - 12 q^{17} + 6 q^{19} + 100 q^{21} + 12 q^{23} - 7400 q^{25} + 116 q^{27} - 2 q^{29} - 8 q^{33} - 748 q^{35} - 2 q^{37} + 8 q^{39} + 438 q^{43} + 140 q^{45} - 12 q^{49} - 8 q^{53} - 284 q^{55} - 108 q^{57} - 2058 q^{59} - 2 q^{61} + 216 q^{63} - 8 q^{65} + 6 q^{67} - 6 q^{69} - 216 q^{71} - 296 q^{73} - 1186 q^{75} - 1372 q^{77} + 10688 q^{81} + 248 q^{85} + 4 q^{87} + 88 q^{89} + 4186 q^{91} - 4220 q^{93} - 500 q^{95} - 8 q^{97} + 13440 q^{99} + O(q^{100}) \)

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

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