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Properties

Label 588.4.q
Level $588$
Weight $4$
Character orbit 588.q
Rep. character $\chi_{588}(85,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $168$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.q (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(588, [\chi])\).

Total New Old
Modular forms 2052 168 1884
Cusp forms 1980 168 1812
Eisenstein series 72 0 72

Trace form

\( 168 q - 6 q^{3} + 16 q^{5} - 8 q^{7} - 252 q^{9} + O(q^{10}) \) \( 168 q - 6 q^{3} + 16 q^{5} - 8 q^{7} - 252 q^{9} + 84 q^{11} - 96 q^{13} - 210 q^{15} + 312 q^{17} + 716 q^{19} + 18 q^{21} - 56 q^{23} - 1008 q^{25} - 54 q^{27} + 504 q^{29} + 288 q^{31} - 120 q^{33} - 1620 q^{35} - 322 q^{37} - 210 q^{39} + 56 q^{41} + 84 q^{43} - 360 q^{45} - 1348 q^{47} - 820 q^{49} - 840 q^{51} - 952 q^{53} + 2746 q^{55} - 252 q^{57} - 764 q^{59} - 782 q^{61} - 198 q^{63} - 1568 q^{65} - 1092 q^{67} - 48 q^{69} + 56 q^{71} - 3208 q^{73} - 1674 q^{75} - 2696 q^{77} - 560 q^{79} - 2268 q^{81} - 5732 q^{83} - 1434 q^{87} + 1424 q^{89} + 5540 q^{91} + 420 q^{93} + 7336 q^{95} + 136 q^{97} - 1008 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)