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Properties

Label 630.4.bi
Level $630$
Weight $4$
Character orbit 630.bi
Rep. character $\chi_{630}(479,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 880 288 592
Cusp forms 848 288 560
Eisenstein series 32 0 32

Trace form

\( 288 q + 1152 q^{4} - 60 q^{9} + O(q^{10}) \) \( 288 q + 1152 q^{4} - 60 q^{9} - 24 q^{11} + 132 q^{14} - 4 q^{15} + 4608 q^{16} + 100 q^{21} - 42 q^{29} - 52 q^{30} + 780 q^{35} - 240 q^{36} - 1116 q^{39} - 618 q^{41} - 96 q^{44} + 696 q^{45} - 252 q^{46} - 198 q^{49} - 792 q^{50} + 1544 q^{51} + 528 q^{56} - 16 q^{60} + 18432 q^{64} + 3696 q^{69} - 36 q^{70} - 6570 q^{75} + 2376 q^{79} - 2468 q^{81} + 400 q^{84} - 7842 q^{89} + 108 q^{90} + 8228 q^{99} + O(q^{100}) \)

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

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