↑

Properties

Label 630.4.cd
Level $630$
Weight $4$
Character orbit 630.cd
Rep. character $\chi_{630}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $576$
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.cd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1760 576 1184
Cusp forms 1696 576 1120
Eisenstein series 64 0 64

Trace form

\( 576 q - 16 q^{6} + O(q^{10}) \) \( 576 q - 16 q^{6} - 48 q^{11} - 168 q^{15} - 9216 q^{16} + 288 q^{17} + 16 q^{18} - 240 q^{21} + 312 q^{23} + 252 q^{27} + 168 q^{30} - 1280 q^{33} - 480 q^{36} + 1236 q^{41} + 872 q^{42} + 2288 q^{45} + 504 q^{46} + 672 q^{50} + 1152 q^{51} - 1056 q^{56} - 2376 q^{57} + 504 q^{58} + 704 q^{60} - 72 q^{61} + 1184 q^{63} + 1152 q^{68} - 64 q^{72} - 5272 q^{75} - 6528 q^{77} - 2848 q^{78} + 1048 q^{81} - 8 q^{87} - 1400 q^{90} - 1248 q^{92} - 6360 q^{93} + 256 q^{96} + O(q^{100}) \)

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

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