Properties

Label 588.4.y
Level $588$
Weight $4$
Character orbit 588.y
Rep. character $\chi_{588}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $336$
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.y (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 4104 336 3768
Cusp forms 3960 336 3624
Eisenstein series 144 0 144

Trace form

\( 336 q + 8 q^{5} + 14 q^{7} + 252 q^{9} + O(q^{10}) \) \( 336 q + 8 q^{5} + 14 q^{7} + 252 q^{9} - 252 q^{11} - 132 q^{13} + 210 q^{15} - 324 q^{17} - 296 q^{19} + 12 q^{21} - 28 q^{23} + 546 q^{25} - 504 q^{29} + 270 q^{31} + 138 q^{33} + 2580 q^{35} + 1204 q^{37} + 2184 q^{39} + 424 q^{41} + 168 q^{43} - 936 q^{45} - 2696 q^{47} - 2732 q^{49} - 2184 q^{51} - 1652 q^{53} - 1234 q^{55} - 84 q^{57} + 6212 q^{59} + 4094 q^{61} + 1008 q^{63} - 784 q^{65} - 168 q^{67} - 1608 q^{69} - 56 q^{71} + 2542 q^{73} - 312 q^{75} + 1940 q^{77} + 350 q^{79} + 2268 q^{81} - 6604 q^{83} + 4260 q^{87} + 3328 q^{89} - 176 q^{91} + 1134 q^{93} + 18956 q^{95} + 15956 q^{97} + 1008 q^{99} + O(q^{100}) \)

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

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