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Properties

Label 630.4.z
Level $630$
Weight $4$
Character orbit 630.z
Rep. character $\chi_{630}(169,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $216$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 630.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 880 216 664
Cusp forms 848 216 632
Eisenstein series 32 0 32

Trace form

\( 216 q + 432 q^{4} + 16 q^{5} + 64 q^{9} + O(q^{10}) \) \( 216 q + 432 q^{4} + 16 q^{5} + 64 q^{9} + 96 q^{11} - 112 q^{14} + 188 q^{15} - 1728 q^{16} - 64 q^{20} + 112 q^{21} + 288 q^{25} - 1112 q^{29} + 176 q^{30} - 144 q^{31} + 896 q^{36} + 584 q^{39} + 512 q^{41} + 768 q^{44} + 1884 q^{45} + 5292 q^{49} + 376 q^{50} + 3884 q^{51} - 1296 q^{54} + 1584 q^{55} + 448 q^{56} - 2584 q^{59} + 352 q^{60} - 13824 q^{64} + 1704 q^{65} - 1040 q^{66} + 5480 q^{69} - 4376 q^{71} - 3568 q^{74} + 2208 q^{75} - 936 q^{79} - 512 q^{80} - 688 q^{81} + 896 q^{84} - 1656 q^{85} + 2048 q^{86} - 1280 q^{89} - 2520 q^{90} - 1008 q^{91} - 2028 q^{95} - 4188 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)