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Properties

Label 630.4.bz
Level $630$
Weight $4$
Character orbit 630.bz
Rep. character $\chi_{630}(13,\cdot)$
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.bz (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

\( 576 q + O(q^{10}) \) \( 576 q - 16 q^{11} - 336 q^{15} + 4608 q^{16} + 16 q^{18} + 240 q^{21} + 104 q^{23} - 672 q^{30} - 2184 q^{35} + 704 q^{36} + 952 q^{42} - 2016 q^{46} - 448 q^{50} - 840 q^{51} - 4480 q^{53} - 352 q^{56} + 5176 q^{57} - 1008 q^{58} - 352 q^{60} + 5196 q^{63} + 232 q^{65} + 1168 q^{71} - 128 q^{72} + 3248 q^{77} - 2848 q^{78} - 3944 q^{81} - 3808 q^{86} + 416 q^{92} + 2880 q^{93} + 1792 q^{95} + 2976 q^{98} + O(q^{100}) \)

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

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