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Properties

Label 315.4.u
Level $315$
Weight $4$
Character orbit 315.u
Rep. character $\chi_{315}(59,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $280$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 315.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

Total New Old
Modular forms 296 296 0
Cusp forms 280 280 0
Eisenstein series 16 16 0

Trace form

\( 280 q - 542 q^{4} - 6 q^{5} + 48 q^{6} + O(q^{10}) \) \( 280 q - 542 q^{4} - 6 q^{5} + 48 q^{6} - 6 q^{10} - 138 q^{14} + 69 q^{15} - 2030 q^{16} - 12 q^{19} + 24 q^{20} - 426 q^{21} - 24 q^{24} - 2 q^{25} + 48 q^{26} + 114 q^{29} + 168 q^{30} - 6 q^{31} + 48 q^{34} + 765 q^{35} + 660 q^{36} - 666 q^{39} - 618 q^{41} + 624 q^{44} - 687 q^{45} + 216 q^{46} - 398 q^{49} + 786 q^{50} + 846 q^{51} + 2220 q^{54} - 90 q^{56} - 6 q^{59} - 924 q^{60} + 48 q^{61} + 14032 q^{64} - 2223 q^{65} + 2922 q^{66} + 1686 q^{69} - 792 q^{70} + 1407 q^{75} + 480 q^{76} + 722 q^{79} - 3855 q^{80} + 156 q^{81} + 4866 q^{84} - 127 q^{85} - 1854 q^{89} + 507 q^{90} + 1364 q^{91} - 6 q^{94} - 453 q^{95} - 4422 q^{96} - 3606 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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