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Properties

Label 315.4.bh
Level $315$
Weight $4$
Character orbit 315.bh
Rep. character $\chi_{315}(169,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $216$
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.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 296 216 80
Cusp forms 280 216 64
Eisenstein series 16 0 16

Trace form

\( 216 q + 432 q^{4} - 8 q^{5} - 32 q^{9} + O(q^{10}) \) \( 216 q + 432 q^{4} - 8 q^{5} - 32 q^{9} - 180 q^{11} + 112 q^{14} - 56 q^{15} - 1728 q^{16} + 282 q^{20} - 56 q^{21} - 396 q^{24} - 144 q^{25} + 544 q^{26} + 904 q^{29} + 380 q^{30} + 72 q^{31} - 396 q^{34} - 2220 q^{36} - 260 q^{39} - 256 q^{41} - 6016 q^{44} - 1908 q^{45} + 72 q^{46} + 5292 q^{49} + 70 q^{50} - 3148 q^{51} + 3876 q^{54} - 792 q^{55} - 1344 q^{56} + 1568 q^{59} + 4608 q^{60} - 15192 q^{64} - 1616 q^{65} + 9256 q^{66} - 4280 q^{69} + 9264 q^{71} + 7796 q^{74} - 6204 q^{75} - 1116 q^{76} + 468 q^{79} + 5144 q^{80} - 688 q^{81} - 1792 q^{84} + 1656 q^{85} - 4828 q^{86} + 640 q^{89} - 8692 q^{90} + 504 q^{91} + 3312 q^{94} + 1340 q^{95} - 14148 q^{96} + 1584 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)