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Properties

Label 588.3.bf
Level $588$
Weight $3$
Character orbit 588.bf
Rep. character $\chi_{588}(47,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2640$
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.bf (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 588 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 2736 2736 0
Cusp forms 2640 2640 0
Eisenstein series 96 96 0

Trace form

\( 2640 q - 26 q^{4} - 14 q^{6} - 26 q^{9} + O(q^{10}) \) \( 2640 q - 26 q^{4} - 14 q^{6} - 26 q^{9} - 22 q^{10} + 9 q^{12} - 56 q^{13} - 26 q^{16} + 27 q^{18} - 50 q^{21} - 24 q^{22} + 16 q^{24} + 960 q^{25} - 188 q^{28} + 5 q^{30} - 22 q^{33} - 308 q^{34} - 22 q^{36} + 268 q^{37} - 534 q^{40} + 156 q^{42} + 98 q^{45} - 92 q^{46} - 112 q^{49} - 316 q^{52} - 176 q^{54} + 70 q^{57} - 122 q^{58} - 648 q^{60} - 436 q^{61} + 112 q^{64} - 392 q^{66} - 140 q^{69} + 260 q^{70} - 198 q^{72} + 316 q^{73} - 644 q^{76} - 832 q^{78} + 294 q^{81} - 554 q^{82} + 1332 q^{84} - 240 q^{85} + 162 q^{88} + 1673 q^{90} - 16 q^{93} + 92 q^{94} - 160 q^{96} + O(q^{100}) \)

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.