↑

Properties

Label 832.4.w
Level $832$
Weight $4$
Character orbit 832.w
Rep. character $\chi_{832}(257,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $164$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 696 172 524
Cusp forms 648 164 484
Eisenstein series 48 8 40

Trace form

\( 164 q - 704 q^{9} + O(q^{10}) \) \( 164 q - 704 q^{9} + 76 q^{13} + 50 q^{17} - 3796 q^{25} + 2 q^{29} - 6 q^{33} + 6 q^{37} + 702 q^{41} - 744 q^{45} + 3428 q^{49} + 8 q^{53} + 1082 q^{61} + 1788 q^{65} - 106 q^{69} + 1380 q^{77} - 5402 q^{81} - 744 q^{85} - 6 q^{89} + 5388 q^{93} - 6 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(832, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)