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Properties

Label 588.3.s
Level $588$
Weight $3$
Character orbit 588.s
Rep. character $\chi_{588}(43,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $672$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 588.s (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(588, [\chi])\).

Total New Old
Modular forms 1368 672 696
Cusp forms 1320 672 648
Eisenstein series 48 0 48

Trace form

\( 672 q - 12 q^{8} + 336 q^{9} + O(q^{10}) \) \( 672 q - 12 q^{8} + 336 q^{9} - 36 q^{10} + 16 q^{13} + 38 q^{14} + 48 q^{16} + 4 q^{20} - 24 q^{21} + 12 q^{22} - 90 q^{24} - 576 q^{25} - 92 q^{26} + 148 q^{28} - 48 q^{30} - 100 q^{32} + 48 q^{33} - 644 q^{34} - 200 q^{37} - 272 q^{38} - 300 q^{40} - 32 q^{41} + 24 q^{42} - 440 q^{44} + 280 q^{46} - 144 q^{48} - 16 q^{49} - 60 q^{50} + 380 q^{52} + 32 q^{53} - 98 q^{56} + 144 q^{57} - 260 q^{58} - 180 q^{60} + 184 q^{61} - 112 q^{62} - 160 q^{65} - 72 q^{66} - 108 q^{68} + 806 q^{70} - 90 q^{72} - 128 q^{73} + 220 q^{74} + 66 q^{76} + 128 q^{77} - 180 q^{78} + 1928 q^{80} - 1008 q^{81} + 40 q^{82} + 48 q^{84} - 288 q^{85} + 1056 q^{86} + 912 q^{88} + 224 q^{89} + 108 q^{90} - 574 q^{92} + 144 q^{93} + 630 q^{94} + 300 q^{96} + 256 q^{97} + 716 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)