↑

Properties

Label 630.4.bq
Level $630$
Weight $4$
Character orbit 630.bq
Rep. character $\chi_{630}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 630.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(630, [\chi])\).

Total New Old
Modular forms 880 288 592
Cusp forms 848 288 560
Eisenstein series 32 0 32

Trace form

\( 288 q + 576 q^{4} + 8 q^{6} - 46 q^{9} + O(q^{10}) \) \( 288 q + 576 q^{4} + 8 q^{6} - 46 q^{9} + 16 q^{11} - 44 q^{14} + 4 q^{15} - 2304 q^{16} - 106 q^{21} + 16 q^{24} - 624 q^{26} + 430 q^{29} - 356 q^{30} - 304 q^{35} + 16 q^{36} - 1516 q^{39} - 1518 q^{41} + 32 q^{44} + 1000 q^{45} + 252 q^{46} - 396 q^{49} - 264 q^{50} + 304 q^{51} + 568 q^{54} - 612 q^{55} - 352 q^{56} + 1416 q^{59} + 512 q^{60} - 18 q^{61} - 18432 q^{64} - 900 q^{65} - 544 q^{66} + 24 q^{69} - 36 q^{70} - 4280 q^{71} - 884 q^{75} + 1188 q^{79} - 4418 q^{81} - 440 q^{84} - 1904 q^{86} + 1446 q^{89} + 332 q^{90} - 1224 q^{94} + 3054 q^{95} - 64 q^{96} - 2236 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)