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Properties

Label 630.4.bt
Level $630$
Weight $4$
Character orbit 630.bt
Rep. character $\chi_{630}(317,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $576$
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.bt (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

\( 576 q - 16 q^{6} + O(q^{10}) \) \( 576 q - 16 q^{6} - 168 q^{15} + 4608 q^{16} - 288 q^{17} - 32 q^{18} - 36 q^{21} + 252 q^{27} + 168 q^{30} + 640 q^{33} - 480 q^{36} + 1236 q^{41} + 872 q^{42} - 1840 q^{45} + 504 q^{46} + 672 q^{50} - 1992 q^{51} - 2376 q^{57} - 1008 q^{58} - 352 q^{60} + 36 q^{61} + 6356 q^{63} - 696 q^{65} - 64 q^{72} + 1832 q^{75} - 3216 q^{77} - 2848 q^{78} + 1972 q^{81} - 7280 q^{87} - 1400 q^{90} - 1248 q^{92} + 4824 q^{93} - 128 q^{96} + O(q^{100}) \)

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

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