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Properties

Label 630.4.cg
Level $630$
Weight $4$
Character orbit 630.cg
Rep. character $\chi_{630}(157,\cdot)$
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.cg (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

\( 576 q + O(q^{10}) \) \( 576 q + 32 q^{11} + 168 q^{15} + 4608 q^{16} - 288 q^{17} - 32 q^{18} + 36 q^{21} - 208 q^{23} + 828 q^{27} - 168 q^{30} + 1920 q^{33} + 1128 q^{35} + 32 q^{36} + 1236 q^{41} - 872 q^{42} - 2736 q^{45} - 504 q^{46} + 224 q^{50} + 1992 q^{51} - 1120 q^{53} + 704 q^{56} - 3224 q^{57} - 1008 q^{58} - 352 q^{60} + 108 q^{61} + 1716 q^{63} + 232 q^{65} + 1168 q^{71} + 64 q^{72} - 3280 q^{77} - 2848 q^{78} + 1972 q^{81} + 336 q^{83} - 3808 q^{86} + 5976 q^{90} + 416 q^{92} + 8520 q^{93} - 896 q^{95} + 384 q^{96} + 2976 q^{98} + O(q^{100}) \)

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

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