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Properties

Label 630.4.bw
Level $630$
Weight $4$
Character orbit 630.bw
Rep. character $\chi_{630}(103,\cdot)$
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.bw (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

\( 576 q + O(q^{10}) \) \( 576 q - 16 q^{11} + 168 q^{15} - 9216 q^{16} - 288 q^{17} + 16 q^{18} + 240 q^{21} + 104 q^{23} - 828 q^{27} - 168 q^{30} + 1128 q^{35} + 32 q^{36} - 1236 q^{41} - 872 q^{42} - 1392 q^{45} - 504 q^{46} + 224 q^{50} - 1152 q^{51} - 1120 q^{53} - 352 q^{56} - 3224 q^{57} + 504 q^{58} + 704 q^{60} + 3504 q^{63} - 464 q^{65} + 1152 q^{68} + 1168 q^{71} + 64 q^{72} - 7104 q^{75} + 32 q^{77} - 2848 q^{78} + 1048 q^{81} - 336 q^{83} + 1904 q^{86} - 7272 q^{87} - 5976 q^{90} + 416 q^{92} - 2664 q^{93} + 1792 q^{95} + 2976 q^{98} + O(q^{100}) \)

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

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